Question 1

For the given solution set $\{2, -1\}$, write a quadratic equation in general form.

Accepted Answer

$x^2 - x - 2 = 0$

Question 2

Find the solution set for the following inequality. Express the answer in interval notation. $(9x + 2)/(x - 5) \leq 3x + 2$

Accepted Answer

$(-\infty, -1/2]$

Question 3

Determine if the following relation is a function. If so, find its domain and range: $\{(1, 11), (1, 22), (2, 8), (3, 10)\}$

Accepted Answer

Not a function

Question 4

Identify if the given table of $x$ and $y$ values represents a function. Also, find the domain and range.

\begin{align*}
\begin{array}{c|c}
x & y \
\hline
-5 & 9 \
-4 & 17 \
-17 & 17 \
\end{array}
\end{align*}

Accepted Answer

Function; Domain: $\{-5, -4, -17\}$; Range: $\{9, 17\}$

Question 5

For the given conditions: Slope $m = 2$, passing through $(-1, -\frac{1}{2})$. Write an equation for the line in slope-intercept form by first going through the point-slope form.

Accepted Answer

$y = 2x + 3/2$

Question 6

For a circle with the following center and radius, find its equation (in standard form).

Center $= (8, -16)$, $r = \sqrt{8}$

Accepted Answer

$(x - 8)^2 + (y + 16)^2 = 8$

Question 7

Given the two functions $f(x) = 71x^2 - 2$, $g(x) = x + 10$, find $f(g(x))$ and identify the domain.

Accepted Answer

$f(g(x)) = 71x^2 + 712x - 20$; Domain: $(-\infty, \infty)$

Question 8

Find out the equation of the parabola in vertex form for the given condition:
(a) Shape of the parabola same as $f(x) = 13x^2$
(b) Vertex of the parabola $(-1, -1)$

Accepted Answer

$y = 13(x + 1)^2 - 1$

Question 9

If $1$ is a zero of the following polynomial function, solve for all the other zeros. $f(x) = x^3 - 13x^2 - 14$.

Accepted Answer

$x = 7 + \sqrt{35}$ and $x = 7 - \sqrt{35}$

Question 10

Determine the end behavior of the graph of the following polynomial function using the Leading Coefficient Test: $f(x) = 2x^4 + 19x^2 - 3x - 2$

Accepted Answer

Graph rises to the left and right

Question 11

A company’s profit $P$ (in thousands of dollars) is modeled by the quadratic function $P(x) = -2x^2 + 8x + 10$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $18$ thousand dollars at $x = 2$ thousand units

Question 12

A population of bacteria triples every 4 hours. If the initial population is 500, what will the population be after 12 hours?

Accepted Answer

$500 	imes 3^3 = 13,500$

Question 13

A quadratic equation $ax^2 + bx + c = 0$ has real and equal roots. Which condition must be satisfied?

Accepted Answer

$b^2 - 4ac = 0$

Question 14

A car rental company charges a flat fee of $\$50$ plus $\$0.20$ per mile driven. If a customer has $\$90$ to spend, what is the maximum number of miles they can drive?

Accepted Answer

$200$ miles

Question 15

Which of the following is the correct equation for a line perpendicular to $y = -\frac{1}{2}x + 3$ and passing through $(4, -2)$?

Accepted Answer

$y = 2x - 10$

Question 16

If $f(x) = x^2 - 4$ and $g(x) = x + 2$, find $(f \circ g)(3)$.

Accepted Answer

$f(g(3)) = 25$

Question 17

A quadratic function $f(x)$ has its vertex at $(2, -3)$ and passes through the point $(4, 5)$. What is its equation in vertex form?

Accepted Answer

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

College Algebra Midterm Study Guide: Key Concepts and Practice

Study Guide - Practice Questions

Study Guide - Flashcards