$$30 \text{ ft} \times 30 \text{ ft}$$

Question 1

Given the quadratic function $$f(x) = -(x-1)^2$ + 4$$, what are the coordinates of the vertex?

Accepted Answer

$$(1, 4)$$

Question 2

For the function $$f(x) = -(x-1)^2$ + 4$$, what is the y-intercept?

Accepted Answer

$$(0, 3)$$

Question 3

Which equation gives the x-coordinate of the vertex for a quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

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

Question 4

If $$a \u003c 0 in $$the quadratic function $$f(x) = ax^2$ + bx + c$$, what can you conclude about the graph?

Accepted Answer

The parabola opens downward and has a maximum value.

Question 5

Given $$f(x) = -x^2$ + 4x + 1$$, what is the x-coordinate of the vertex?

Accepted Answer

$$x = 2$$

Question 6

For $$f(x) = -x^2$ + 4x + 1$$, what is the maximum value of the function?

Accepted Answer

$$5$$

Question 7

What are the x-intercepts of $$f(x) = -x^2$ + 4x + 1$$?

Accepted Answer

$$x \approx -0.2$$ and $$x \approx 4.2$$

Question 8

A rectangular region is to be enclosed with 120 feet of fencing. What are the dimensions that maximize the area?

Accepted Answer

$$30 	ext{ ft} 	imes 30 	ext{ ft}$$

Question 9

For the quadratic function $$f(x) = 4x^2$ - 16x + 1000$$, what is the minimum value and where does it occur?

Accepted Answer

Minimum value is $$984 at$$ $$x = 2$$

Question 10

What is the range of $$f(x) = 4x^2$ - 16x + 1000$$?

Accepted Answer

$$[984, \infty)$$

Question 11

If a quadratic function is written as $$f(x) = a(x-h)^2$ + k$$, what is the axis of symmetry?

Accepted Answer

$$x = h$$

Question 12

For $$f(x) = ax^2$ + bx + c$$, what is the y-intercept?

Accepted Answer

$$c$$

Question 13

Which of the following best describes the domain of any quadratic function?

Accepted Answer

$$(-\infty, \infty)$$

Question 14

If $$f(x) = a(x-h)^2$ + k$$ and $$a \u003e 0$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$k$$

Question 15

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its maximum or minimum at $$x = -\frac{b}{2a}. $$What is the value of $$f(x) at $$this point?

Accepted Answer

$$f\left(-\frac{b}{2a}\right)$$

Question 16

If the quadratic function $$f(x) = ax^2$ + bx + c is $$used to model the area of a rectangle with fixed perimeter, what does the vertex represent?

Accepted Answer

The maximum area and the dimensions that yield it.

Question 17

Which step is NOT part of graphing a quadratic function in standard form?

Accepted Answer

Finding the slope of the tangent at the vertex.

Question 18

If $$f(x) = ax^2$ + bx + c$$ and $$a \u003e 0$$, which statement is true?

Accepted Answer

The function has a minimum value at the vertex.

Question 19

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

Accepted Answer

$$x = 2$$

Question 20

If you are given a quadratic function $$f(x) = ax^2$ + bx + c$$ and asked to maximize or minimize a real-world quantity, what is the first step?

Accepted Answer

Identify which quantity is to be maximized or minimized.

Quadratic Functions: Graphs, Properties, and Applications

Study Guide - Practice Questions