Question 1

Which of the following intervals represents all real numbers $x$ such that $x$ is greater than or equal to $1$ and strictly less than $6$?

Accepted Answer

$[1, 6)$

Question 2

A quadratic equation $ax^2 + bx + c = 0$ has a negative discriminant. What can you conclude about its solutions?

Accepted Answer

There are two complex (imaginary) solutions.

Question 3

Given the function $f(x) = 2x^2 - 8x + 7$, what is the vertex of the parabola?

Accepted Answer

$(2, -1)$

Question 4

Which of the following best describes the solution set for the inequality $x^2 < 9$?

Accepted Answer

$(-3, 3)$

Question 5

A chemical reaction requires the temperature $T$ (in $^\circ$C) to satisfy $20 < T \leq 48$. Which interval notation correctly represents the possible values for $T$?

Accepted Answer

$(20, 48]$

Question 6

Solve for $x$: $2x^2 - 7x + 3 = 0$

Accepted Answer

$x = 3, x = \dfrac{1}{2}$

Question 7

A company wants to fence a rectangular area of $2400$ m$^2$ such that the length is twice the width. What are the dimensions of the rectangle?

Question 8

Which of the following is the correct factorization of $x^2 - 7x + 12$?

Accepted Answer

$(x - 3)(x - 4)$

Question 9

If $f(x) = x^2 + 2x + 1$, what is the value of $f(-3)$?

Accepted Answer

$4$

Question 10

A projectile is launched from the ground with an initial velocity of $20$ m/s. Its height $h$ (in meters) after $t$ seconds is given by $h(t) = -4.9t^2 + 20t$. After how many seconds does the projectile reach its maximum height?

Accepted Answer

$2.04$ seconds

Question 11

Which of the following is the solution set for $|2x - 5| < 7$?

Question 12

If the quadratic equation $x^2 + bx + 16 = 0$ has exactly one real solution, what is the value of $b$?

Accepted Answer

$\pm 8$

Question 13

Which of the following describes the range of the function $f(x) = x^2 - 4$?

Accepted Answer

$[-4, \infty)$

Question 14

A population of bacteria triples every hour. If the initial population is $100$, what will the population be after $4$ hours?

Accepted Answer

$2700$

Question 15

Which of the following is the solution to the system of equations: $\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$?

Accepted Answer

$(3, 2)$

Question 16

If $f(x) = 3x - 2$ and $g(x) = x^2$, what is $(f \circ g)(2)$?

Accepted Answer

$10$

Question 17

Which of the following is the correct solution to the inequality $2x + 5 > 11$?

Accepted Answer

$x > 3$

Question 18

A quadratic function models the height of a ball thrown upward from a $25$ m building: $h(t) = -5t^2 + 20t + 25$. After how many seconds does the ball hit the ground?

Accepted Answer

$5.74$ seconds

Question 19

Which of the following is the domain of the function $f(x) = \dfrac{1}{x-3}$?

Accepted Answer

$x 
eq 3$

Question 20

If $x$ is a real number such that $x^2 + 4x + 8 = 0$, what is the nature of its solutions?

Accepted Answer

Two complex (imaginary) solutions

College Algebra Study Guidance: Intervals, Quadratic Equations, and Complex Numbers

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