Question 1

Given the quadratic function $$f(x) = x^2$ + 10x + 23$$, what are the coordinates of the vertex?

Accepted Answer

$$(-5, -2)$$

Question 2

For the function $$g(x) = \frac{x^2$}{2} - 4x + 8$$, what is the axis of symmetry?

Accepted Answer

$$x = 4$$

Question 3

Which of the following statements is true about the graph of $$f(x) = -2(x-1)^2$ + 3$$?

Accepted Answer

The vertex is at $$(1, 3)$$ and the graph opens downward.

Question 4

A landscaper has 24 ft of stone to enclose a rectangular pond against a wall. If the width is $$w$$, what is the length in terms of $$w$$?

Accepted Answer

$$24 - 2w$$

Question 5

For the pond problem, what value of $$w$$ maximizes the area?

Accepted Answer

$$w = 6$$

Question 6

What is the maximum area that can be enclosed by the pond described above?

Accepted Answer

$$72$$ square feet

Question 7

Given $$f(x) = a(x-h)^2$ + k$$, which statement is always true?

Accepted Answer

The axis of symmetry is $$x = h.$$

Question 8

If a quadratic function opens downward, which of the following must be true?

Accepted Answer

The coefficient $$a is $$negative.

Question 9

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

Accepted Answer

$$(-\infty, 5]$$

Question 10

Which interval describes where the function $$f(x) = -2(x-7)^2$ + 2 is $$increasing?

Accepted Answer

$$(-\infty, 7)$$

Question 11

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 19.6t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$21.6$$ meters

Question 12

Which of the following is the correct method to find the vertex of $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

Set $$x = -\frac{b}{2a}$$ and substitute into $$f(x).$$

Question 13

If $$f(x) = 2(x-3)^2$ + 4$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$4$$

Question 14

Which transformation occurs when the graph of $$f(x) = x^2$ is changed to g(x$$) = \frac{1}{2}$$x^2$$?

Accepted Answer

Vertical shrink

Question 15

Given $$f(x) = (x+1)^2$ - 9$$, what is the axis of symmetry?

Accepted Answer

$$x = -1$$

Question 16

A quadratic function has its vertex at $$(3, -4)$$ and opens upward. Which could be its equation?

Accepted Answer

$$f(x) = (x-3)^2$ - 4$$

Question 17

If the quadratic function $$f(x) = ax^2$ + bx + c$$ has $$a \u003c 0$$, what can you say about its range?

Accepted Answer

$$(-\infty, k]$$ for some $$k$$

Question 18

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

Accepted Answer

The area of a rectangular garden with a fixed perimeter.

Question 19

If $$f(x) = x^2$ + bx + c$$ has its minimum at $$x = -3$$, what is the value of $$b$$?

Accepted Answer

$$6$$

Question 20

Which of the following best describes the interval where $$f(x) = (x-2)^2$ + 1 is $$decreasing?

Accepted Answer

$$(-\infty, 2)$$

Quadratic Functions and Their Graphs: Vertex, Axis of Symmetry, and Applications

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