Question 1

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

Accepted Answer

$$f(x) = a(x - h)^2$ + k$$

Question 2

Given the quadratic function $$f(x) = -2(x + 3)^2$ + 5$$, what is the vertex of the parabola?

Accepted Answer

$$(-3, 5)$$

Question 3

For the quadratic function $$f(x) = 3x^2$ - 6x + 2$$, what is the axis of symmetry?

Accepted Answer

$$x = 1$$

Question 4

A company models its profit with the quadratic function $$P(x) = -4x^2$ + 40x + 100$$, where $$x is $$the number of units sold. What is the maximum profit, and at how many units sold does it occur?

Accepted Answer

Question 5

Which statement is true about the graph of $$f(x) = -x^2$ + 4x + 1$$?

Accepted Answer

The parabola opens downward and has a maximum at its vertex.

Question 6

If the quadratic function $$f(x) = ax^2$ + bx + c$$ has $$a \u003e 0$$, what can be said about its minimum or maximum?

Accepted Answer

It has a minimum at the vertex.

Question 7

Find the $$x-$$intercepts of the quadratic function $$f(x) = x^2$ - 5x + 6.$$

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 8

A farmer has 120 meters of fencing to enclose a rectangular field. What dimensions maximize the area, and what is the maximum area?

Accepted Answer

Dimensions: $$30 by$$ $$30$$ meters; Area: $$900$$ square meters

Question 9

Given $$f(x) = 2(x - 4)^2$ - 7$$, what is the range of the function?

Accepted Answer

$$[-7, \infty)$$

Question 10

For the quadratic function $$f(x) = -x^2$ + 4x + 1$$, what is the domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$(-\infty, 5]$$

Question 11

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

Accepted Answer

It determines the direction and width of the parabola.

Question 12

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$x = 3$$ and opens upward. Which of the following must be true?

Accepted Answer

$$a \u003e 0$$

Question 13

Given $$f(x) = 4x^2$ - 16x + 1000$$, what is the minimum value of the function?

Accepted Answer

$$984$$

Question 14

If a parabola has its vertex at $$(2, -5)$$ and opens downward, which of the following could be its equation?

Accepted Answer

$$f(x) = -(x - 2)^2$ - 5$$

Question 15

Which of the following is the correct process to find the $$y-$$intercept of $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

Set $$x = 0$$ and solve for $$f(0)$$

Question 16

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 17

Which of the following is NOT a characteristic of the graph of a quadratic function?

Accepted Answer

It can be a straight line.

Question 18

If $$f(x) = a(x - h)^2$ + k$$ and $$a \u003c 0$$, which statement is true?

Accepted Answer

The parabola opens downward and has a maximum at $$(h, k).$$

Question 19

Which real-world scenario can be modeled by a quadratic function?

Accepted Answer

The area of a rectangular garden with a fixed perimeter.

Quadratic Functions: Graphing, Properties, and Applications

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