Question 1

Given the quadratic equation $$2x^2 - 4x + 3 = 0$, use the discriminant to determine the number and type of solutions.

Accepted Answer

Two complex (non-real) solutions

Question 2

Solve the quadratic equation $$x^2 - 6x + 9 = 0$ and select the correct solution.

Accepted Answer

$$x = 3 ($$with multiplicity 2)

Question 3

A ball is thrown upward from the ground with an initial velocity of $$20 m/s. $$Its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t. $$When does the ball hit the ground again?

Accepted Answer

$$t = 4$$ seconds

Question 4

Given the function $$f(x) = |x-2| + 1$$, what is the vertex of its graph?

Accepted Answer

$$(2, 1)$$

Question 5

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 6

Given the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 0 \ 2x-1 & x \geq 0 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$-1 ($$since $$f(-3) = -3 + 2)$$

Question 7

What is the equation of the line passing through the point $$(1, 2)$$ with slope $$-3 in $$point-slope form?

Accepted Answer

$$y - 2 = -3(x - 1)$$

Question 8

Find the equation of a line parallel to $$y = 2x - 5$$ that passes through $$(0, 4).$$

Accepted Answer

$$y = 2x + 4$$

Question 9

If $$f(x) = x^2$, what is the graph of g(x$$) = $$(x-3)^2 + 2$ in relation to f(x$$)$$?

Accepted Answer

Shifted right 3 units and up 2 units

Question 10

Which transformation is applied to $$f(x) = \sqrt{x} to $$obtain $$g(x) = \sqrt{x+4} - 2$$?

Accepted Answer

Shift left 4 units and down 2 units

Question 11

Find the inverse of the function $$f(x) = 3x + 5.$$

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x-5}{3}$$

Question 12

What is the distance between the points $$(2, -1)$$ and $$(-2, 3)$$?

Accepted Answer

$$2\sqrt{8}$$

Question 13

Write the standard form of the equation of a circle with center $$(3, -2)$$ and radius $$5.$$

Accepted Answer

$$(x-3)^2$$ + $$(y+2)^2 = 25$

Question 14

Given the function $$f(x) = \dfrac{1}{x-4}$$, what is its domain?

Accepted Answer

$$x 
eq 4$$

Question 15

Which of the following best describes the symmetry of the function $$f(x) = x^4$?

Accepted Answer

Even function; symmetric about the $$y-$$axis

Question 16

A circle has the equation $$x^2$$ + $$y^2 - 6x + 8y = 0$. What are its center and radius?

Accepted Answer

Center $$(3, -4)$$, radius $$5$$

Question 17

Given the function $$f(x) = x^2$ - 4x + 3$$, what are its $$x-$$intercepts?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 18

If a line has slope $$\dfrac{1}{2}$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$-2$$

Question 19

What is the range of the function $$f(x) = \sqrt{x-1}$$?

Accepted Answer

$$[0, \infty)$$

Question 20

Given the function $$f(x) = \begin{cases} 2x+1 & x \u003c 1 \ x^2$ & x \geq 1 \end{cases}$$, what is $$f(2)$$?

Accepted Answer

$$5$$

College Algebra: Key Concepts and Methods Study Guide

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