Question 1

Which of the following is the general form of a quadratic function?

Accepted Answer

$$f(x) = ax^2$ + bx + c$$

Question 2

Given the quadratic function $$f(x) = -2(x + 1)^2$ + 3$$, what is the vertex of the parabola?

Accepted Answer

$$( -1, 3 )$$

Question 3

For the quadratic function $$f(x) = 2x^2$ - 4x + 1$$, what is the equation of the axis of symmetry?

Accepted Answer

$$x = 1$$

Question 4

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 5

Which of the following statements is true about the graph of $$f(x) = -x^2$ + 4x - 3$$?

Accepted Answer

The parabola opens downward and has a maximum point.

Question 6

If the vertex of a parabola is at $$(3, -2)$$ and the axis of symmetry is $$x = 3$$, which of the following could be its equation?

Accepted Answer

$$f(x) = a(x - 3)^2$ - 2$$

Question 7

Given $$f(x) = x^2$ - 6x + 8$$, what is the range of $$f(x)$$?

Accepted Answer

$$[ -1, \infty )$$

Question 8

A company models its profit $$P(x) in $$thousands of dollars by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold in thousands. How many units should be sold to maximize profit?

Accepted Answer

$$x = 2$$

Question 9

Which of the following best describes the effect of the coefficient $$a in $$the quadratic function $$f(x) = a(x - h)^2$ + k$$?

Accepted Answer

It determines whether the parabola opens upward or downward and affects the width of the parabola.

Question 10

For the quadratic function $$f(x) = 3(x + 2)^2$ - 5$$, what is the domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[ -5, \infty )$$

Question 11

Given $$f(x) = -x^2$ + 2x + 3$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$3$$

Question 12

If a quadratic function has its vertex at $$( -4, 9 )$$ and opens upward, which of the following statements is true?

Accepted Answer

The minimum value of the function is $$9.$$

Question 13

Which of the following is the correct formula for the axis of symmetry of the quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

$$x = \frac{ -b }{ 2a }$$

Question 14

A quadratic function models the height of a projectile: $$h(t) = -16t^2$ + 32t + 5. At $$what time $$t$$ does the projectile reach its maximum height?

Accepted Answer

$$t = 1$$

Question 15

Given $$f(x) = x^2$ - 4$$, which of the following is true about its graph?

Accepted Answer

The vertex is at $$(0, -4)$$ and the parabola opens upward.

Question 16

If $$f(x) = -3x^2$ + 6x - 1$$, what is the maximum value of $$f(x)$$?

Accepted Answer

$$2$$

Question 17

Which of the following real-world scenarios can be modeled by a quadratic function?

Accepted Answer

The height of a ball thrown in the air as a function of time.

Question 18

For the quadratic function $$f(x) = 2x^2$ + 8x + 7$$, what is the vertex?

Accepted Answer

$$( -2, -1 )$$

Question 19

If the graph of $$f(x) = a(x - h)^2$ + k is $$reflected over the $$x-$$axis, what happens to the value of $$a$$?

Accepted Answer

The sign of $$a is $$reversed.

Quadratic Functions: Graphing and Analysis

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