Question 1

Which of the following is the standard form of the equation of a circle with center at $$(-1, 4)$$ and radius $$3$$?

Accepted Answer

$$(x + 1)^2$ + (y - 4)^2$ = 9$$

Question 2

Given the quadratic function $$y = -2x^2$ + 10x - 3$$, what are the coordinates of the vertex?

Accepted Answer

$$(2.5, 9.5)$$

Question 3

A ball is thrown upward from ground level with an initial velocity of $$144 ft/sec. $$Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 144t. $$What is the maximum height reached by the ball?

Accepted Answer

$$324 ft$$

Question 4

Which of the following is a possible rational zero of the polynomial $$f(x) = x^3$ - 2x^2$ + 3x - 6$$?

Accepted Answer

$$1$$

Question 5

Given $$f(x) = 2x^2$ - 3x + 7$$ and $$g(x) = x - 2$$, find $$f(g(3)).$$

Accepted Answer

$$8$$

Question 6

Which of the following describes the axis of symmetry for the quadratic function $$y = x^2$ - 6x + 5$$?

Accepted Answer

$$x = 3$$

Question 7

If $$f(x) = x^2$ - 4x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$21$$

Question 8

Which of the following is the correct synthetic division result for dividing $$4x^3$$ - $$3x^2 + 2x - 5$ by x - 1$?

Accepted Answer

$$4x^2 + x + 3$ remainder -2$

Question 9

For the rational function $$f(x) = \dfrac{2x^2$ - 3x + 1}{x - 5}$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 5$$

Question 10

Given the function $$f(x) = x^2$ - 2x + 1$$, which of the following ordered pairs is on its graph?

Accepted Answer

$$(3, 4)$$

Question 11

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

Accepted Answer

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

Question 12

If $$f(x) = 2x^2$ - 3x + 7$$, what is $$f(-1)$$?

Accepted Answer

$$12$$

Question 13

Which of the following is the correct equation for a circle with center $$(2, -5)$$ and radius $$4$$?

Accepted Answer

$$(x - 2)^2$ + (y + 5)^2$ = 16$$

Question 14

Given $$f(x) = x^2$ - 4x + 1$$ and $$g(x) = 2x + 3$$, find $$f(g(2)).$$

Accepted Answer

$$49$$

Question 15

Which of the following is a horizontal asymptote for the rational function $$f(x) = \dfrac{3x^2$ + 2x - 1}{x^2$ - 4}$$?

Accepted Answer

$$y = 3$$

Question 16

If $$f(x) = x^2$ - 2x + 1$$, what is the value of $$f(5)$$?

Accepted Answer

$$16$$

Question 17

Which of the following is the correct remainder when $$x^3$$ - $$4x^2 + 5x - 8$ is divided by x - 2$ using synthetic division?

Accepted Answer

$$-8$$

Question 18

For the quadratic function $$y = -x^2$ + 6x - 5$$, what is the axis of symmetry?

Accepted Answer

$$x = 3$$

Question 19

Which of the following is the correct set of possible rational zeros for $$f(x) = x^3$ + 2x^2$ - 3x - 6$$?

Accepted Answer

$$\pm1, \pm2, \pm3, \pm6$$

College Algebra Study Notes: Circles, Functions, Quadratics, Polynomials, and Rational Functions

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