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 function $f(x) = 3x^2 - 12x + 7$, what is the axis of symmetry?

Accepted Answer

$x = 2$

Question 4

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

Accepted Answer

$21.6$ meters

Question 5

Which transformation occurs to the graph of $f(x) = x^2$ to obtain $g(x) = (x - 4)^2 + 2$?

Accepted Answer

Shift right 4 units and up 2 units

Question 6

If a parabola opens downward and has its vertex at $(1, 7)$, which of the following could be its equation?

Accepted Answer

$f(x) = -2(x - 1)^2 + 7$

Question 7

Given $f(x) = x^2 - 6x + 8$, what are the $x$-intercepts of the function?

Accepted Answer

$(2, 0)$ and $(4, 0)$

Question 8

Which of the following best describes the domain and range of $f(x) = -x^2 + 3$?

Accepted Answer

Domain: $(-\infty, \infty)$, Range: $(-\infty, 3]$

Question 9

A quadratic function in standard form is $f(x) = ax^2 + bx + c$. What is the formula for the $x$-coordinate of the vertex?

Accepted Answer

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

Question 10

Which method is most appropriate for solving $x^2 - 9 = 0$?

Accepted Answer

Square root property

Question 11

If $f(x) = 2(x + 1)^2 - 4$, what is $f(0)$?

Accepted Answer

$-2$

Question 12

A parabola has its vertex at $(2, -3)$ and passes through the point $(3, 1)$. If its equation is $f(x) = a(x - 2)^2 - 3$, what is the value of $a$?

Accepted Answer

$4$

Question 13

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

Accepted Answer

It opens downward and has a maximum value.

Question 14

Given $f(x) = (x - 2)^2 + 1$, for which values of $x$ is the function increasing?

Accepted Answer

$x > 2$

Question 15

Which of the following is the correct process to convert $f(x) = x^2 + 8x + 5$ to vertex form?

Accepted Answer

Complete the square: $f(x) = (x + 4)^2 - 11$

Question 16

A real-world scenario: The profit $P(x)$ (in dollars) from selling $x$ units of a product is modeled by $P(x) = -5x^2 + 200x - 1000$. How many units should be sold to maximize profit?

Accepted Answer

$x = 20$

Question 17

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

Accepted Answer

If $|a| > 1$, the parabola is narrower; if $0 < |a| < 1$, it is wider.

Question 18

Given $f(x) = -3(x + 2)^2 + 4$, what is the range of the function?

Accepted Answer

$(-\infty, 4]$

Question 19

If $f(x) = (x - 1)^2 - 9$, what is the $y$-intercept of the function?

Accepted Answer

$-8$

Quadratic Functions: Properties, Vertex Form, and Transformations

Study Guide - Practice Questions

Study Guide - Flashcards