The graph shrinks vertically by a factor of $3$

The graph shifts right $2$ units

Question 1

Given the function $f(x) = x^2 - 4$, for which values of $x$ is $f(x)$ negative?

Accepted Answer

$-2 < x < 2$

Question 2

What are the zeroes of the quadratic function $f(x) = 2x^2 - 3x - 2$?

Accepted Answer

$x = -0.5$ and $x = 2$

Question 3

For the function $f(x) = x^2 - 4$, what is the vertex of the parabola?

Accepted Answer

$(0, -4)$

Question 4

A golf ball's height after $t$ seconds is given by $s(t) = -16t^2 + 64t + 4$. For what interval of $t$ is the ball higher than $52$ ft above ground?

Accepted Answer

$1 < t < 3$

Question 5

A circle has an area of at least $225\pi$. What is the minimum possible diameter of the circle?

Accepted Answer

$15$

Question 6

Which transformation shifts the graph of $f(x) = |x|$ two units to the right?

Accepted Answer

$f(x) = |x-2|$

Question 7

What is the effect of multiplying the function $f(x) = |x|$ by $\frac{1}{3}$?

Accepted Answer

The graph shrinks vertically by a factor of $3$

Question 8

Given the function $f(x) = |x+4| - 1$, what is the vertex of the graph?

Accepted Answer

$(-4, -1)$

Question 9

If the graph of $f(x) = \sqrt{x}$ is reflected over the $x$-axis, shifted up $2$ units, and right $2$ units, what is the equation of the new graph?

Accepted Answer

$f(x) = -\sqrt{x-2} + 2$

Question 10

For the quadratic $f(x) = 2x^2 - 3x - 2$, for which intervals is $f(x) \leq 0$?

Accepted Answer

$-0.5 \leq x \leq 2$

Question 11

Which of the following describes a vertical shift of the graph $f(x) = |x|$ up by $2$ units?

Accepted Answer

$f(x) = |x| + 2$

Question 12

If $f(x) = x^2 - 4$, what is the $y$-intercept of the graph?

Accepted Answer

$(0, -4)$

Question 13

Which transformation will move the vertex of $f(x) = |x|$ to $(-2, 2)$?

Accepted Answer

$f(x) = |x+2| + 2$

Question 14

Which equation represents a horizontal shrink of $f(x) = |x|$ by a factor of $3$?

Accepted Answer

$f(x) = |3x|$

Question 15

For the function $f(x) = x^2 - 4$, when is $f(x) \geq 0$?

Accepted Answer

$x \leq -2$ or $x \geq 2$

Question 16

If the graph of $f(x) = |x|$ is shifted left $4$ units and down $1$ unit, what is the equation of the new graph?

Accepted Answer

$f(x) = |x+4| - 1$

Question 17

Which of the following is the correct factored form of $x^2 - 4$?

Accepted Answer

$(x-2)(x+2)$

Question 18

If $f(x) = |x|$, what is the effect of replacing $x$ with $x-2$ in the function?

Accepted Answer

The graph shifts right $2$ units

Question 19

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

Accepted Answer

$(0, -2)$

Quadratic Functions, Inequalities, and Transformations of Graphs

Study Guide - Practice Questions