Question 1

Given the quadratic function $f(x) = -3(x+4)^2 + 9$, what are the coordinates of its vertex?

Accepted Answer

$(-4, 9)$

Question 2

For the function $f(x) = 4(x+1)^2 - 3$, what is the range of $f(x)$?

Accepted Answer

$[-3, \infty)$

Question 3

Which of the following describes the domain of the quadratic function $f(x) = -3(x-8)^2 + 3$?

Accepted Answer

$(-\infty, \infty)$

Question 4

A parabola opens downward and has a vertex at $(8, 3)$. What is the maximum value of the function?

Accepted Answer

$3$

Question 5

Given $f(x) = -3(x-8)^2 + 3$, what is the $y$-intercept of the function?

Accepted Answer

$(0, -9)$

Question 6

For the function $f(x) = 4(x+1)^2 - 3$, what is the axis of symmetry?

Accepted Answer

$x = -1$

Question 7

If a parabola has a vertex at $(-4, 9)$ and opens downward, which of the following best describes its range?

Accepted Answer

$(-\infty, 9]$

Question 8

Which of the following is the correct equation for a parabola with vertex $(3, -3)$ that opens upward and passes through $(5, 1)$?

Question 9

Given the function $f(x) = -3(x-8)^2 + 3$, what is the direction in which the parabola opens?

Accepted Answer

Downward

Question 10

If the vertex of a parabola is at $(1, -3)$ and the parabola opens upward, what is the minimum value of the function?

Accepted Answer

$-3$

Question 11

A quadratic function $f(x)$ has no $x$-intercepts. Which of the following could be the vertex and direction of opening?

Accepted Answer

Vertex $(0, 17)$, opens upward

Question 12

For the function $f(x) = 4(x+1)^2 - 3$, what is the $y$-intercept?

Question 13

Which of the following best describes the effect of the coefficient $-3$ in $f(x) = -3(x+4)^2 + 9$?

Accepted Answer

It makes the parabola open downward and narrower.

Question 14

If $f(x) = a(x-h)^2 + k$ and $a < 0$, what can you say about the vertex?

Accepted Answer

It is a maximum point.

Question 15

Given the function $f(x) = -3(x-8)^2 + 3$, what is the axis of symmetry?

Accepted Answer

$x = 8$

Quadratic Functions and Parabolas: Graphs, Properties, and Applications

Study Guide - Practice Questions