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What are the solutions of 3×2 + 14x + 16 = 0? |
A. |
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The only solution of the equation x2 + bx + 16 = 0 is x = 4. What is the value of b? |
b = -8 |
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Which function has zeros at x = −2 and x = 5? |
f(x) = x2 − 3x − 10 |
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An equation has solutions of m = -5 and m = 9. Which could be the equation? |
(m + 5)(m – 9) = 0 |
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What are the solutions to x2 + 8x + 7 = 0? |
x = -7 and x = -1 |
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Which equations are true for x = -2 and x = 2? Check all that apply. |
x2 – 4 = 0 4×2 = 16 |
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Which function has zeros at x = 10 and x = 2? |
f(x) = x2 – 12x + 20 |
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John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width. Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic? |
w(w + 2) = 48 |
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For what values of x is x2 + 2x = 24 true? |
4 and -6 |
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What is the only solution of 2×2 + 8x = x2 – 16? |
-4 |
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Which is a solution to (x − 2)(x + 10) = 13? |
x = 3 |
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Which is a solution to the equation? (x −2)(x + 5) = 18 |
x = −7 |
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Which is a solution to (x – 3)(x + 9) = -27? |
x = 0 |
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What are the solutions to the equation? x2 + 6x = 40 |
x = −10 and x = 4 |
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Two factors of -48 have a difference of 19. The factor with a greater absolute value is positive. What is the sum of the factors? |
13 |
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What are the solutions to the quadratic equation x2 – 16 = 0? |
x = 4 and x = -4 |
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What are the solutions to the quadratic equation 3(x − 4)2 = 75? |
x = −1 and x = 9 |
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What are the solutions of the quadratic equation (x + 3)2 = 49? |
x = 4 and x = -10 |
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What are the solution(s) to the quadratic equation x2 – 25 = 0? |
x = 5 and x = -5 |
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Which are the roots of the quadratic function f(b) = b2 – 75? Check all that apply. |
1and 2 |
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Theo started to solve the quadratic equation (x + 2)2 – 9 = -5. He added 9 to both sides and the resulting equation was Which was the resulting equation of that step? |
x + 2 = ±2 |
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Which are the roots of the quadratic function f(q) = q2 – 125? Check all that apply. |
1 and 2 |
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What are the solution(s) of the quadratic equation 98 – x2 = 0? |
C. |
|
What are the solutions to the quadratic equation (5y + 6)2 = 24? |
A. |
|
What value of c makes x2 − 24x + c a perfect square trinomial? |
144 |
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Solve x2 + 14x = −24 by completing the square. What is the solution set of the equation? |
{−12, −2} |
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Solve x2 – 8x = 3 by completing the square. Which is the solution set of the equation? |
A. |
|
Which are the solutions of x2 = 19x + 1? |
B. |
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What value of c makes x2 − 12x + c a perfect square trinomial? |
36 |
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Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation? |
D. |
|
What value of c makes x2 + 6x + c a perfect square trinomial? |
9 |
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Which are the solutions of x2 = -7x – 8? |
D. |
|
Atraeus is solving the quadratic equation by completing the square. What is the value of A. |
7 |
|
What are the zeros of the quadratic function f(x)=2×2-10x-3 |
C |
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Sienne is solving the quadratic equation by completing the square. What is the value of A. |
3 |
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Patel is solving 8×2+16x+3=0 check all that apply |
1,2,5 |
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The first few steps in solving the quadratic equation 8×2+80x=-5 by completing the square are shown. |
200 |
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Atraeus is solving the quadratic equation by completing the square. 7×2 – 14x + 6 = 0 7×2 – 14x = -6 A(x2 – 2x) = -6 What is the value of A? |
7 |
|
What are the zeros of the quadratic function f(x) = 2×2 – 10x – 3? |
c. |
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Isoke is solving the quadratic equation by completing the square. 10×2 + 40x – 13 = 0 10×2 + 40x = 13 A(x2 + 4x) = 13 What is the value of A? |
10 |
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Sunil is solving the quadratic equation by completing the square. What should sunil do next. |
C. |
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What are the zeros of the quadratic function f(x)=2×2+16x-9 |
Not b |
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What are the zeros of the quadratic function f(x)=6×2+12x-7 |
Not d |
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What are the zeros of the quadratic function f(x)=16×2+32x-9 |
B. |
|
Lie is solving a quadratic equation by completing the square. What should lie do next |
B. |
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Which is a zero of the quadratic function f(x)=9×2-54x-19 |
Not b |
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In which step did yvonne make a mistake. |
A. |
|
In which step did tran first make an error. |
Not d |
|
What should gio do first. |
A. |
|
What should maya do first |
C. |
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Which statement is true about the quadratic equation 8×2 − 5x + 3 = 0? |
The leading coefficient is 8. |
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Determine the discriminant for the quadratic equation 0 = -2×2 + 3. Based on the discriminant value, how many real number solutions does the equation have? Discriminant = b2 – 4ac |
2 |
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The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown. Step 1: -c = ax2 + bx Which best explains or justifies Step 1? |
subtraction property of equality |
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What are the values of a, b, and c in the quadratic equation -2×2 + 4x – 3 = 0? |
a = -2, b = 4, c = – 3 |
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What is the value of the discriminant for the quadratic equation -3 = -x2 + 2x? Discriminant = b2 – 4ac |
not c |
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What are the values of a, b, and c in the quadratic equation 0 = 5x – 4×2 – 2? |
a = -4, b = 5, c = -2 |
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Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3×2 – 2x + 6 into the quadratic formula? Quadratic formula: x = |
not c or b |
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What is the value of the discriminant for the quadratic equation 0 = 2×2 + x – 3? Discriminant = b2 – 4ac |
not a |
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Which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3×2 + 1 into the quadratic formula? Quadratic formula: |
not d |
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What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has? |
The discriminant is −4, so the equation has no real solutions |
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What is the value of the discriminant for the quadratic equation 0 = x + 2 + x2? Discriminant = b2 – 4ac |
-7 |
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Which shows the correct substitution of the values a, b, and c from the equation -2 = -x + x2 – 4 into the quadratic formula? Quadratic formula: x = |
not c |
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A student is deriving the quadratic formula. Her first two steps are shown. Step 1: -c = ax2 + bx Step 2: Which best explains or justifies Step 2? |
factoring the binomial |
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Alessandro wrote the quadratic equation -6 = x2 + 4x – 1 in standard form. What is the value of c in his new equation? |
not -1 |
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Some of the steps in the derivation of the quadratic formula are shown. Step 4: Step 5: Step 6: Step 7: Which best explains why the expression cannot be rewritten as during the next step? |
not d |
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Which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3×2 + 1 into the quadratic formula? Quadratic formula: |
a. |
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What are the values of a, b, and c in the quadratic equation 0 = x2 – 3x – 2? |
a =1/2 , b = -3, c = -2 |
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Some of the steps in the derivation of the quadratic formula are shown. Step 3: -c + = a Step 4a: -c + = a Step 4b: + = a Which best explains or justifies Step 4b? |
converting to a common denominator |
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Anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation x2 + 4x + 8 = 0. Which explanation could Anderson provide? |
The equation has one real number solution because the discriminant is 0 |
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Rhett is solving the quadratic equation 0= x2 – 2x – 3 using the quadratic formula. Which shows the correct substitution of the values a, b, and c into the quadratic formula? |
D. |
|
Zacharias is using the quadratic formula to solve the equation 0 = -2×2 + 5x – 3. He begins by substituting as shown. Quadratic formula: x = |
not a |
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Ramiya is using the quadratic formula to solve a quadratic equation. Her equation is x = after substituting the values of a, b, and c into the formula. Which is Ramiya’s quadratic equation? Quadratic formula: x = |
0 = x2 + 3x + 2 |
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What is the discriminant of the quadratic equation 3 – 4x = -6×2? |
not a |
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Quincy uses the quadratic formula to solve for the values of x in a quadratic equation. He finds the solution, in simplest radical form, to be x = . Which best describes how many real number solutions the equation has? |
not b or c |
|
In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x? Quadratic formula: x = |
not c |
|
What is the discriminant of the quadratic equation 0 = 2×2 + 3x – 5? |
not c |
|
What are the zeros of the function f(x) = x2 + 5x + 5 written in simplest radical form? Quadratic formula: x = |
c |
|
A quadratic equation of the form 0 = ax2 + bx + c has a discriminant value of 0. How many real number solutions does the equation have? |
1 |
|
A quadratic equation has a discriminant of 12. Which could be the equation? |
0 = 2×2 + 6x + 3 |
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Nathaniel is using the quadratic formula to solve 0 = x2 + 5x – 6. His steps are shown below. What are the solutions to the equation? |
x = -6, 1 |
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A quadratic equation has exactly one real number solution. Which is the value of its discriminant? |
not c or d |
|
In simplest radical form, what are the solutions to the quadratic equation 0 = -3×2 – 4x + 5? Quadratic formula: x = |
not b |
|
What is the discriminant of the quadratic equation 0 = -x2 + 4x – 2? |
8 |
|
What is the discriminant of the quadratic equation 0 = 2×2 + 3x – 5? |
not b or c |
|
A quadratic equation of the form 0 = ax2 + bx + c has a discriminant value of -16. How many real number solutions does the equation have? |
not 2 or 1 |
|
What is the positive solution to the equation 0 = -x2 + 2x + 1? Quadratic formula: x = |
not b |
|
What is the value of the discriminant of the quadratic equation −1 = 5×2 −2x, and what does its value mean about the number of real number solutions the equation has? |
not c |
|
Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3×2 – 7x + 4 has. Which best describes the discriminant and the number of zeros? |
The equation has two zeros because the discriminant is greater than 0. |
|
Which function has real zeros at x = −10 and x = −6? |
f(x) = x2 + 16x + 60 |
|
What are the solutions to the quadratic equation 4(x + 2)2 = 36 |
x = −5 and x = 1 |
|
Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation? |
{-7, 1} |
|
What is a solution to (x + 6)(x + 2) = 60? |
x = 4 |
|
What are the zeros of the quadratic function f(x) = 2×2 + 8x – 3? |
A. |
|
Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is -99. Which equation can be used to find m, the midpoint of the two numbers? |
m2 – 100 = -99 |
|
Mariya is solving the quadratic equation by completing the square. 4×2 – 20x + 3 = 0 4×2 – 20x = -3 A(x2 – 5x) = -3 What is the value of A? |
4 |
|
Mischa wrote the quadratic equation 0 = -x2 + 4x – 7 in standard form. What is the value of c in her equation? |
-7 |
|
Liliana decides to crop a square photo 2 inches on each side to fit it into a frame. The area of the original photo was 121 square inches. In the equation (x + 2)2 = 121, x represents the side measure of the cropped photo. What are the dimensions of the cropped photo? |
9 inches by 9 inches |
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Which is the graph of a quadratic equation that has a negative discriminant? |
D. |
|
Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = -6. Which function could Heather be writing? |
f(x) = -x2 – 12x – 36 |
|
The first step in solving the quadratic equation -5×2 + 8 = 133 is to subtract from each side. |
8 |
|
The first few steps in solving the quadratic equation 5×2 + 27x = 14 − 13x by completing the square are shown. 5×2 + 27x = 14 − 13x 5×2 + 40x = 14 5(x2 + 8x) = 14 Which is the best step to do next to solve the equation by completing the square? |
5(x2 + 8x + 16) = 94 |
|
Which is a solution to the equation? (x − 3)(x − 5) = 35 |
x = 10 |
|
Solve x2 − 24x = −80 by completing the square. What is the solution set of the equation? |
{4, 20} |
|
What is the value of the discriminant of the quadratic equation −2×2 = −8x + 8, and what does its value mean about the number of real number solutions the equation has? |
The discriminant is equal to 0, which means the equation has one real number solution. |
|
The function g(x) is defined as g(x) = 6×2 + 23x – 4. When does g(x) = 0? |
B. |
|
Solve x2 – 8x = 20 by completing the square. Which is the solution set of the equation? |
{-2, 10} |
|
What are the solutions to m2 – 9 = 0? |
m = -3 and m = 3 |
|
A quadratic equation of the form 0 = ax2 + bx + c has one real number solution. Which could be the equation? |
0 = -2×2 – 4x – 2 |
|
Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = -6. Which function could Heather be writing? |
f(x) = -x2 – 12x – 36 |
|
A quadratic equation has zero real number solutions. Which could be the discriminant value associated with this equation? |
-5 |
|
Between which two ordered pairs does the graph of f(x) = x2 + x – 9 cross the negative x-axis? Quadratic formula: x = |
(-6, 0) and (-5, 0) |
|
Sergey is solving 5×2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation? Check all that apply. |
2,3,and4 |
|
What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2×2 − 3x + 8, and what does it mean about the number of real solutions the equation has? |
The discriminant is 73, so the equation has 2 real solutions. |
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