Modeling And Analyzing Quadratic Functions - Part One Unit Review

The domain of a quadratic function is all real numbers and the range is y ≤ 2. How many x-intercepts does the function have?

2

What is the range of the function f(x) = 3x^2 + 6x - 8? {y|y ≥ -1} {y|y ≤ -1} {y|y ≥ -11} {y|y ≤ -11}

{y|y ≥ -11}

Over which interval is the graph of f(x) = -x2 + 3x + 8 increasing? (-∞, 1.5) (-∞, 10.25) (1.5, ∞) (10.25, ∞)

(-∞, 1.5)

A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. The path of the projectile is modeled using the equation h(t) = -16t2 + 48t + 190. What is the maximum height of the projectile? 82 feet 190 feet 226 feet 250 feet

226 feet

The axis of symmetry for the function f(x) = -2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located? (0, 1) (1, 3) (1, 7) (2, 1)

(1, 3)

What is the vertex of the function f(x) = 1/2x^2 + 3x + 3/2?

(-3, -3)

Over which interval is the graph of f(x) = 1/2x^2 + 5x + 6 increasing? (-6.5, ∞) (-5, ∞) (-∞, -5) (-∞, -6.5)

(-5, ∞)

Use the drop-down menus to describe the key aspects of the function f(x) = -x2 - 2x - 1. The vertex is the __________. minimum value maximum value y-intercept The function is increasing __________. when x < -1 when x > -1 for all real numbers of x for no values of x The function is decreasing __________. when x < -1 when x > -1 for all real numbers of x for no values of x The domain of the function is ____________. all real numbers all real numbers less than -1 all negative real numbers all positive real numbers. The range of the function is _____________. all real numbers all real numbers less than -1 all numbers less than or equal to 0 all numbers greater than or equal to 0

The vertex is the maximum value. The function is increasing when x < -1. The function is decreasing when x > -1. The domain of the function is all real numbers. The range of the function is all numbers less than or equal to 0.

What is the x-intercept of the graph of the function f(x) = x^2 − 16x + 64? (−8, 0) (0, 8) (8, 0) (0, −8)

(8, 0)

The axis of symmetry for the graph of the function f(x) = 1/4x^2 + bx + 10 is x=6. What is the value of b? −12 −3 1/2 3

-3

The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply. The vertex is the maximum value. The axis of symmetry is x = -4. The domain is all real numbers. The range is all real numbers. The function is increasing over (-∞, -4). The x-intercepts are at (-6, 0) and (-2, 0).

✓The axis of symmetry is x = -4. ✓The domain is all real numbers. ✓The x-intercepts are at (-6, 0) and (-2, 0).

Mathieu is finding the x-intercepts of the function f(x) = x^2 + 4x + 3. His work is shown below. 1. 0 = x^2 + 4x + 3 2. 0 = (x + 3)(x + 1) 3. x + 3 = x + 1 4. x = x - 2 5. 0 = -2 6. There are no x-intercepts. Which error did Mathieu make? He factored incorrectly. He did not use the constant as the x-intercept. He set the factored expressions equal to each other. He incorrectly solved the equation x + 3 = x + 1.

He set the factored expressions equal to each other.

The a value of a function in the form f(x) = ax^2 + bx + c is negative. Which statement must be true? The vertex is a maximum. The y-intercept is negative. The x-intercepts are negative. The axis of symmetry is to the left of zero.

The vertex is a maximum.

Which statements about the graph of the function f(x) = -x2 - 4x + 2 are true? Select three options. The domain is {x|x ≤ -2}. The range is {y|y ≤ 6}. The function is increasing over the interval (-∞ , -2). The function is decreasing over the interval (−4, ∞). The function has a positive y-intercept.

✓The range is {y|y ≤ 6}. ✓The function is increasing over the interval (-∞ , -2). ✓The function has a positive y-intercept.

Which statements about the graph of the function f(x) = 2x^2 - x - 6 are true? Select two options. The domain of the function is {x|x ≥ 1/4}. The range of the function is all real numbers. The vertex of the function is (1/4, -6 1/8) . The function has two x-intercepts. The function is increasing over the interval (-6 1/8, ∞).

✓The vertex of the function is (1/4, -6 1/8) . ✓The function has two x-intercepts.

Consider the function f(x) = x^2 + 2x - 15. What are the x-intercepts of the function? Left-most x-intercept: (___, 0) Right-most x-intercept: (___, 0)

Left-most x-intercept: (-5, 0) Right-most x-intercept: (3, 0)

Which must be true of a quadratic function whose vertex is the same as its y-intercept? The axis of symmetry for the function is x = 0. The axis of symmetry for the function is y = 0. The function has no x-intercepts. The function has 1 x-intercept.

The axis of symmetry for the function is x = 0.

The graph of which function will have a maximum and a y-intercept of 4? f(x) = 4x^2 + 6x - 1 f(x) = -4x^2 + 8x + 5 f(x) = -x^2 + 2x + 4 f(x) = x^2 + 4x - 4

f(x) = -x^2 + 2x + 4

Which functions have an axis of symmetry of x = -2? Check all that apply. f(x) = x^2 + 4x + 3 f(x) = x^2 - 4x - 5 f(x) = x^2 + 6x + 2 f(x) = -2x^2 - 8x + 1 f(x) = -2x^2 + 8x - 2

✓f(x) = x2 + 4x + 3 ✓f(x) = -2x2 - 8x + 1