$h(1) = -16(1)^2 + 32(1) + 5 = 21$

Shift left 3 units and up 2 units

Domain: $(-\infty, \infty)$, Range: $[1, \infty)$

Question 1

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

Accepted Answer

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

Question 2

Given the quadratic function $f(x) = 2x^2 + 3x - 7$, what is the degree of the polynomial?

Accepted Answer

$2$

Question 3

For the quadratic function $f(x) = a(x - h)^2 + k$, what is the vertex of the parabola?

Accepted Answer

$(h, k)$

Question 4

If the graph of $f(x) = -x^2 + 4x - 5$ opens downward, which value of $a$ causes this?

Accepted Answer

$a < 0$

Question 5

What is the axis of symmetry for the quadratic function $f(x) = 3(x + 2)^2 - 5$?

Accepted Answer

$x = -2$

Question 6

A ball is thrown and its height is modeled by $h(t) = -16t^2 + 32t + 5$. What is the maximum height reached by the ball?

Accepted Answer

$h(1) = -16(1)^2 + 32(1) + 5 = 21$

Question 7

Which transformation occurs when the function $f(x) = (x - 3)^2 + 2$ is compared to $f(x) = x^2$?

Accepted Answer

Shift left 3 units and up 2 units

Question 8

Given $f(x) = -2(x + 1)^2 + 6$, what is the vertex and does the parabola have a maximum or minimum?

Accepted Answer

Vertex $(-1, 6)$, maximum

Question 9

What is the domain and range of $f(x) = x^2 + 1$?

Accepted Answer

Domain: $(-\infty, \infty)$, Range: $[1, \infty)$

Question 10

A company models its profit by $P(x) = -x^2 + 6x + 7$, where $x$ is the number of items sold. How many items should be sold to maximize profit?

Accepted Answer

$x = 3$

Question 11

Convert $f(x) = x^2 + 6x + 7$ to vertex form.

Accepted Answer

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

Question 12

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

Accepted Answer

$x = 1$

Question 13

Which method is best to use for solving $f(x) = x^2 + 3x + 2$ for its roots?

Accepted Answer

Factoring

Question 14

If $f(x) = a(x - h)^2 + k$ and $|a| < 1$, what effect does this have on the graph?

Accepted Answer

Vertical compression

Question 15

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

Accepted Answer

$f(0) = 8$

Question 16

A parabola has vertex $(3, -2)$ and opens upward. Which equation could represent its function?

Accepted Answer

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

Question 17

Which of the following describes the interval where $f(x) = x^2$ is increasing?

Accepted Answer

$x > 0$

Question 18

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

Accepted Answer

$(-\infty, 4]$

Question 19

If a parabola opens downward and has a vertex at $(0, 5)$, what is the maximum value of the function?

Accepted Answer

$5$

Question 20

Which of the following is NOT a property of all quadratic functions?

Accepted Answer

They always open upward.

Quadratic Functions: Properties, Vertex Form, and Transformations

Study Guide - Practice Questions