Q: Given the function $f(x) = 3x - 2$ for $x < -1$ and $f(x) = 4 - x^2$ for $x \\geq -1$, which of the following describes the graph at $x = -1$?

There is a jump discontinuity at $x = -1$

Q: If $f(x) = 0$ has no real solutions for a quadratic function, what does this imply about the graph?

The graph does not intersect the $x$-axis

Question 1

Given the quadratic function $f(x) = -4(x - 7)^2 + 11$, what is the vertex of the parabola?

Accepted Answer

$(7, 11)$

Question 2

For the function $f(x) = x^2 + 3x - 2$, does the parabola open upwards or downwards?

Accepted Answer

Upwards

Question 3

If the graph of a quadratic function does not intersect the $x$-axis, what can you say about its discriminant?

Accepted Answer

The discriminant is negative

Question 4

Solve for $x$: $4x^2 = 108$

Accepted Answer

$x = 3$ or $x = -3$

Question 5

A company produces brake rotors. The total revenue function is $R(x) = 4x - 20$ and the total cost function is $C(x) = 0.002x^2 + 0.8x + 50$. What is the profit function $P(x)$?

Accepted Answer

$P(x) = 4x - 20 - (0.002x^2 + 0.8x + 50)$

Question 6

Given the function $f(x) = 3x - 2$ for $x < -1$ and $f(x) = 4 - x^2$ for $x \geq -1$, which of the following describes the graph at $x = -1$?

Accepted Answer

There is a jump discontinuity at $x = -1$

Question 7

If $f(x) = 0$ has no real solutions for a quadratic function, what does this imply about the graph?

Accepted Answer

The graph does not intersect the $x$-axis

Question 8

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

Accepted Answer

$37$ feet

Question 9

For the quadratic function $y = 4.97x^2 - 0.126x$, is the graph concave up or down?

Accepted Answer

Concave up

Question 10

The cost to cater a dinner meeting is given by $C(x) = \begin{cases} 300 & 	ext{if } 0 < x \leq 30 \ 300 + 12(x - 30) & 	ext{if } x > 30 \end{cases}$, where $x$ is the number of meals served. What is $C(60)$?

Accepted Answer

$660$

Question 11

Given the quadratic function $f(x) = ax^2 + bx + c$, what is the formula for the axis of symmetry?

Accepted Answer

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

Question 12

If the range of a quadratic function is $y \geq -3$, what does this tell you about the vertex?

Accepted Answer

The vertex is at the minimum point $(-3)$

Question 13

A company’s profit function is $P(x) = -0.002x^2 + 3.2x - 70$. How many units must be produced and sold to maximize profit?

Accepted Answer

$x = 800$

Question 14

For the quadratic equation $x^2 + 6x + 9 = 0$, how many real solutions are there?

Accepted Answer

One real solution

Question 15

If the axis of symmetry of a parabola is $x = 2$, which of the following could be the equation of the parabola?

Accepted Answer

$y = a(x - 2)^2 + k$

Question 16

A quadratic function models the height of a ball: $h(t) = -16t^2 + 32t + 5$. When does the ball hit the ground?

Accepted Answer

$t = 2.21$ seconds

Question 17

If the cost function for a company is $C(x) = 0.002x^2 + 0.8x + 50$ and the revenue function is $R(x) = 4x - 20$, what is the break-even point?

Accepted Answer

$x \approx 15$ units

Question 18

For the function $y = 4.97x^2 - 0.126x$, what percent is projected for 2026 if $x$ is the number of years after 2000?

Accepted Answer

$y = 4.97(26)^2 - 0.126(26) \approx 3357.6$

College Algebra: Quadratic Functions, Equations, and Applications Study Guide

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