# Quadratic Functions Unit Test

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 f(x)=a(x-h)^2+k Vertex of a quadratic function (formula) What is the axis of symmetry and vertex for the function f(x) = 3(x – 2)2 + 4? x = 2 Vertex: (2, 4) Which best describes the transformation from the graph of f(x) = x2 to the graph of f(x) = (x – 3)2 – 1? left 3 units, down 1 unit left 3 units, up 1 unit right 3 units, down 1 unit right 3 units, up 1 unit right 3 units, down 1 unit The parent function of the function g(x) = (x – h)2 + k is f(x) = x2. The vertex of the function g(x) is located at (9, -8). What are the values of h and k? g(x) = (x – )^2 + 9 -8 What is the equation of the translated function? f(x) = (x – 1)2 – 5 f(x) = (x + 1)2 + 5 f(x) = (x – 5)2 – 1 f(x) = (x + 5)2 + 1 f(x) = (x + 1)2 + 5 Consider the graph of the function f(x) = 2(x + 3)2 + 2. Over which interval is the graph decreasing? (-∞, -3) (-∞, 2) (-3, ∞) (2, ∞) (-∞, -3) Which are characteristics of the graph of the function f(x) = (x + 1)2 + 2? Check all that apply. The domain is all real numbers. The range is all real numbers greater than or equal to 1. The y-intercept is 3. The graph of the function is 1 unit up and 2 units to the left from the graph of y = x2. The graph has two x-intercepts. The domain is all real numbers. The y-intercept is 3. Justine graphs the function f(x) = (x – 7)2 – 1. On the same grid, she graphs the function g(x) = (x + 6)2 – 3. Which transformation will map f(x) on to g(x)? left 13 units, down 2 units right 13 units, down 2 units left 13 units, up 2 units right 13 units, up 2 units left 13 units, down 2 units The graph of which function is decreasing over the interval (-4, ∞)? f(x) = (x + 4)2 + 4 f(x) = -(x + 4)2 + 4 f(x) = (x – 4)2 – 4 f(x) = -(x – 4)2 – 4 f(x) = (x – 4)2 – 4 – INCORRECT What is the equation of the translated function, g(x), if f(x) = x2? g(x) = (x + 5)2 + 2 g(x) = (x + 2)2 + 5 g(x) = (x – 2)2 + 5 g(x) = (x – 5)2 + 2 g(x) = (x – 5)2 + 2 Over what interval is the graph of f(x) = -(x + 8)2 – 1 decreasing? (-8, ∞) Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x – 2)2 + 3? right 2, up 3 Which function has a range of {y|y ≤ 5}? f(x) = -(x – 4)2 + 5 What value represents the vertical translation from the graph of the parent function f(x) = x2 to the graph of the function g(x) = (x + 5)2 + 3? 3 The graph of f(x) = x2 is translated to form g(x) = (x – 2)2 – 3. Which graph represents g(x)? A Sanjay begins to correctly graph the function f(x) = (x + 1)2 – 3. Based on the axis of symmetry and the vertex, which graph could be Sanjay’s? C Which function could be represented by the graph on the coordinate plane? f(x) = (x – 8)2 + 6 f(x) = (x + 8)2 + 6 f(x) = (x + 8)2 – 6 f(x) = (x – 8)2 – 6 f(x) = (x – 8)2 – 6 What is the y-intercept of the quadratic function f(x) = (x – 8)(x + 3)? (8,0) (0,3) (0,-24) (-5,0) (0,-24) What is the midpoint of the x-intercepts of f(x) = (x – 2)(x – 4)? (-3,0) (-1,0) (1,0) (3,0) (3,0) Which function has two x-intercepts, one at (0, 0) and one at (4, 0)? f(x) = x(x − 4) f(x) = x(x + 4) f(x) = (x − 4)(x − 4) f(x) = (x + 4)(x + 4) f(x) = x(x − 4) Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)? (0,6) (0,-6) (6,0) (-6,0) (-6,0) What is the axis of symmetry of the function f(x) = -(x + 9)(x – 21)? The axis of symmetry is x = 6 The graph of the function f(x) = (x – 4)(x + 1) is shown below. Which statement about the function is true? The function is increasing for all real values of x where x < 0. The function is increasing for all real values of x where x < -1 and where x > 4. The function is decreasing for all real values of x where -1 < x < 4. The function is decreasing for all real values of x where x < 1.5. The function is decreasing for all real values of x where x < 1.5. Which is the graph of f(x) = -(x + 3)(x + 1)? B The graph of the function f(x) = -(x + 6)(x + 2) is shown below. Which statement about the function is true? The function is increasing for all real values of x where x < -4. The function is increasing for all real values of x where -6 < x < -2. The function is decreasing for all real values of x where x < -6 and where x > -2. The function is decreasing for all real values of x where x < -4. The function is increasing for all real values of x where x < -4. The axis of symmetry for the graph of the function is f(x) = x2 + bx + 10 is x = 6. What is the value of b? -3 The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph? (−5, 41) (−5, 56) (−5, 76) (−5, 91) (−5, 41) The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the graph? (−9, −2) (−17, −2) (−2, −17) (−2, −9) (−2, −9) The graph of which function has a y-intercept of 3? A Which is the graph of f(x) = x2 – 2x + 3? NOT C, C IS INCORRECT The graph of which function has an axis of symmetry at x = 3? d The axis of symmetry for the graph of the function f(x) = 3×2 + bx + 4 is x = . What is the value of b? -9 Tempestt graphs a function that has a maximum located at (-4, 2). Which could be her graph? C What are the x-intercepts of the graph of the function f(x) = x2 + 4x – 12? (-6, 0), (2,0) (-2, -16), (0, -12) (-6, 0), (-2, -16), (2, 0) (0, -12), (-6, 0), (2, 0) (-6, 0), (2,0) liana started to evaluate the function f(x) = 2×2 – 3x + 7 for the input value 2. f(x) = 2(2)2 – 3(2) + 7 = 2(4) – 3(2) + 7 What is the value of the function when x = 2? 9 10 16 17 9 When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown? 2 + 7c – 4c2 – 3c + 4 -4c2 + 4c + 6 -7c2 + 10c + 6 -4c2 + 4c + 8 -7c2 + 7c + 6 -4c2 + 4c + 6 1 2 3 5 6 8 9 10 Mary throws a plastic disc to her friend, which her friend catches six seconds after Mary throws it. The table shows the height of the disc at one-second intervals. Assuming that the throw represents projectile motion, what are the missing values in the table? A = 5, B = 3 A = 4, B = 0 A = 4, B = 3 A = 5, B = 0 A = 4, B = 3 Which quadratic function is represented by the table? f(x) = 3×2 + 2x – 5 f(x) = 3×2 – 2x + 5 f(x) = 2×2 + 3x – 5 f(x) = 2×2 – 2x + 5 f(x) = 3×2 – 2x + 5 Consider the quadratic function f(y) = 8y2 – 7y + 6. What is the constant of the function? 6 What is f(-3) for the function f(a) = -2a2 – 5a + 4? 1 Which quadratic function has a leading coefficient of 2 and a constant term of -3? f(x) = 2×3 – 3 f(x) = -3×2 – 3x + 2 f(x) = -3×3 + 2 f(x) = 2×2 + 3x – 3 f(x) = 2×2 + 3x – 3 Which represents a quadratic function? f(x) = 2×3 + 2×2 – 4 f(x) = -7×2 – x + 2 f(x) = -3x + 2 f(x) = 0x2 + 3x – 3 f(x) = -7×2 – x + 2 What is true about the function h(x) = x2 + 20x – 17? Check all that apply. The vertex of h is (-10, -117). The vertex form of the function is h(x) = (x + 20)2 – 17. The maximum value of the function is -17. To graph the function h, shift the graph of f(x) = x2 left 10 units and down 117 units. The axis of symmetry of function h is x = 20. The vertex of h is: (-10, -117). To graph the function h, shift the graph of f(x) = x² left 10 units and down 117 units. The function g(x) = 3×2 − 12x + 7 written in vertex form is g(x) = 3(x − 2)2 − 5. What is the vertex of g(x)? (−6, −5) (−2, −5) (2, −5) (6, −5) (2, −5) The function g(x) = -x2 + 16x – 44 written in vertex form is g(x) = -(x – 8)2 + 20. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = -x2 + 16x – 44? The graph of f(x) = x2 is widened. The graph of f(x) = x2 is shifted left 8 units. The graph of f(x) = x2 is shifted down 44 units. The graph of f(x) = x2 is reflected over the x-axis. The graph of f(x) = x2 is reflected over t The function h(x) = -2×2 + 8x written in vertex form is h(x) = -2(x – 2)2 + 8. The function h(x) is shown on the graph along with the parent function, f(x) = x2. Which statement is true concerning the vertex and axis of symmetry of h(x)? The vertex is at (0, 0) and the axis of symmetry is x = 2. The vertex is at (0, 0) and the axis of symmetry is y= 2. The vertex is at (2, 8) and the axis of symmetry is x = 2. The vertex is at (2, 2) and the axis of symmetry is y = 2. The vertex is at (2, 8) and the axis of symmetry is x = 2. Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2? g(x) = -9(x2 + 2x + 1) – 7 g(x) = 4(x2 – 6x + 9) + 1 g(x) = -3(x2 – 8x + 16) – 6 g(x) = 8(x2 – 6x + 9) – 5 g(x) = 8(x2 – 6x + 9) – 5 The function g(x) = -3×2 – 36x – 60 written in vertex form is g(x) = -3(x + 6)2 + 48. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = -3×2 – 36x – 60? The graph of f(x) = x2 is made narrower. The graph of f(x) = x2 is shifted right 6 units. The graph of f(x) = x2 is shifted down 48 units. The graph of f(x) = x2 is reflected over the y-axis. The graph of f(x) = x2 is made narrower. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4×2 + 24x + 30? The graph of f(x) = x2 is widened. The graph of f(x) = x2 is shifted left 3 units. The graph of f(x) = x2 is shifted up 30 units. The graph of f(x) = x2 is reflected over the x-axis. The graph of f(x) = x2 is shifted left 3 units. What is f(x) = 8×2 + 4x written in vertex form? f(x) = 8 – f(x) = 8 – f(x) = 8 – 2 f(x) = 8 – 4 A What is f(x) = 2×2 + 28x – 5 written in vertex form? f(x) = 2(x + 7)2 – 19 f(x) = 2(x + 7)2 – 103 f(x) = 2(x + 14)2 – 14 f(x) = 2(x + 14)2 – 98 f(x) = 2(x + 7)2 – 103 The first three steps in writing f(x) = 40x + 5×2 in vertex form are shown. Write the function in standard form. f(x) = 5×2 + 40x Factor a out of the first two terms. f(x) = 5(x2 + 8x) Form a perfect square trinomial. = 16 f(x) = 5(x2 + 8x + 16) – 5(16) What is the function written in vertex form? f(x) = 5(x + 4) – 80 f(x) = 5(x + 8) – 80 f(x) = 5(x + 4)2 – 80 f(x) = 5(x + 8)2 – 80 f(x) = 5(x + 4)2 – 80 The function g(x) = 10×2 – 100x + 213 written in vertex form is g(x) = 10(x – 5)2 – 37. Which statements are true about g(x)? Check all that apply. The axis of symmetry is the line x = -5. The vertex of the graph is (5, -37). The parabola has a minimum. The parabola opens up. The value of a, when the equation is written in vertex form, is negative. The vertex of the graph is (5, -37). The parabola has a minimum. The parabola opens up. Which function in vertex form is equivalent to f(x) = x2 + 6x + 3? f(x) = (x + 3)2 + 3 f(x) = (x + 3)2 − 6 f(x) = (x + 6)2 + 3 f(x) = (x + 6)2 − 6 f(x) = (x + 3)2 − 6 Which zero pair could be added to the function so that the function can be written in vertex form? 3, -3 6, -6 9, -9 36, -36 36, -36 Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x? f(x) = (x – 1)2 + 3 f(x) = (x – 1)2 + 5 f(x) = (x + 1)2 + 3 f(x) = (x + 1)2 + 5 f(x) = (x – 1)2 + 3 Which value is needed to create a perfect square trinomial from the expression x2 + 8x + _____? 16 The function f(x) = x2 + 10x – 3 written in vertex form is f(x) = (x + 5)2 – 28. What are the coordinates of the vertex? (-5, -28) (-5, 28) (5, -28) (5, 28) (-5, -28) Which statements are true about the graph of the function f(x) = 6x – 4 + x2? Check all that apply. The vertex form of the function is f(x) = (x – 2)2 + 2. The vertex of the function is (-3, -13). The axis of symmetry for the function is x = 3. The graph increases over the interval (-3, ). The function does not cross the x-axis. The vertex of the function is (-3, -13). The graph increases over the interval (-3, ). What value for c will make the expression a perfect square trinomial? x2 – 7x + c 49/4 Charla wants to determine the vertex of the function f(x) = x2 – 18x + 60 by changing the function into vertex form. Which statement about the vertex of the function is true? The x-coordinate of the vertex is greater than the y-coordinate. The x-coordinate of the vertex is negative. The y-coordinate of the vertex is greater than the y-intercept. The y-coordinate of the vertex is positive. The x-coordinate of the vertex is greater than the y-coordinate. How many unit tiles need to be added to the expression x2 + 4x + 3 in order to form a perfect square trinomial? 1 Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = -8x + x2 + 7 ? left 4, down 9 left 4, up 23 right 4, down 9 right 4, up 23 right 4, down 9 The function g(x) is a translation of f(x) = (x + 3)2 – 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which function could be g(x)? g(x) = (x – 2)2 + k g(x) = (x + 8)2 + k g(x) = (x – h)2 – 5 g(x) = (x – h)2 – 15 g(x) = (x – 2)2 + k Which function has a vertex on the y-axis? f(x) = (x – 2)2 f(x) = x(x + 2) f(x) = (x – 2)(x + 2) f(x) = (x + 1)(x – 2) f(x)= (x-2)(x+2) What is the y-value of the vertex of the function f(x) = -(x + 8)(x – 14)? The y-value of the vertex is y = 121 Gerald graphs the function f(x) = (x – 3)2 – 1. Which statements are true about the graph? Check all that apply. The domain is {x| x ≥ 3}. The range is {y| y ≥ -1}. The function decreases over the interval (-∞, 3). The function increases over the interval (-1, ∞). The axis of symmetry is x = -1. The vertex is (3, -1). The range is {y| y ≥ -1}. The function decreases over the interval (-∞, 3). The vertex is (3, -1). Which function has a vertex on the y-axis? f(x) = (x – 2)2 f(x) = x(x + 2) f(x) = (x – 2)(x + 2) f(x) = (x + 1)(x – 2) f(x) = (x – 2)(x + 2) The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)? g(x) = (x − 7)2 − 3 g(x) = (x + 7)2 − 3 g(x) = (x − 3)2 − 7 g(x) = (x − 3)2 + 7 g(x) = (x + 7)2 − 3 Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2? right 5, down 23 left 5, down 23 right 5, up 27 left 5, up 27 right 5, down 23 The graph of the function f(x) = (x + 2)(x − 4) is shown. Which describes all of the values for which the graph is negative and increasing? all real values of x where x < −2 all real values of x where −2 < x < 4 all real values of x where 1 < x < 4 all real values of x where x < 0 all real values of x where 1 < x < 4 What is the axis of symmetry of h(x) = 6×2 − 60x + 147? x = −5 x = −3 x = 3 x = 5 x = 5 Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 6x + 6? left 3 units, down 3 units right 3 units, down 3 units left 6 units, down 1 unit right 6 units, down 1 unit right 3 units, down 3 units The graph of the function f(x) = −3×2 − 3x + 6 is shown. Which statements describe the graph? Check all that apply. The vertex is the maximum value. The axis of symmetry is x = . The domain is all real numbers. The range is all real numbers. The x-intercepts are at (−2, 0) and (1,0). The function is decreasing from (−∞, 6.75). The vertex is the maximum value. The axis of symmetry is x = . The domain is all real numbers. The x-intercepts are at (−2, 0) and (1,0). What is the y-value of the vertex of the function f(x) = -(x – 3)(x + 11)? The y-value of the vertex is 49 What are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36? (−4, 0) and (9, 0) (4, 0) and (−9, 0) (−3, 0) and (12, 0) (3, 0) and (−12, 0) (4, 0) and (−9, 0)

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