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 $$x^2$$ \u003c 9$$?

Accepted Answer

$$(-3, 3)$$

Question 5

A chemical reaction requires the temperature $$T (in$$ $$^\circC) to $$satisfy $$20 \u003c T \leq 48. $$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?

Accepted Answer

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 $$|2x - 5| \u003c 7$$?

Accepted Answer

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 $$2x + 5 \u003e 11$$?

Accepted Answer

$$x \u003e 3$$

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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