Question 1

Which of the following functions is symmetric with respect to the y-axis?

Accepted Answer

$$f(x) = x^2$

Question 2

Given the function $$f(x) = -2(x-3)^2$ + 5$$, which transformation was applied to the parent function $$f(x) = x^2$?

Accepted Answer

Shifted right 3 units, reflected over the x-axis, stretched vertically by 2, shifted up 5 units

Question 3

Which equation represents a parabola that opens downward and has its vertex at $$(2, -4)$$?

Accepted Answer

$$y = -(x-2)^2$ - 4$$

Question 4

If $$f(x) = x^2$ and g(x) = x + 1$, what is the composition f(g(x$$))$$?

Accepted Answer

$$f(g(x)) = (x+1)^2$

Question 5

Which of the following is the correct factored form of $$x^2 - 5x + 6$?

Accepted Answer

$$(x-2)(x-3)$$

Question 6

Solve the quadratic equation $$x^2 - 4x - 5 = 0$ by factoring.

Accepted Answer

$$x = -5, x = 1$$

Question 7

A ball is thrown upward from the top of a building. Its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 24t + 10. $$What is the maximum height reached by the ball?

Accepted Answer

$$h = 39.4$$ meters

Question 8

Which of the following is the solution to the quadratic equation $$2x^2 + 3x - 2 = 0$ using the Quadratic Formula?

Accepted Answer

$$x = \frac{-3 \pm \sqrt{25}}{4}$$

Question 9

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

Accepted Answer

$$x^2 + 2x + 1$

Question 10

Which of the following describes the domain of $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

All real numbers except $$x = 3$$

Question 11

A quadratic equation $$ax^2 + bx + c = 0$ has no real solutions if:

Accepted Answer

$$b^2 - 4ac$$ \u003c 0$$

Question 12

Which of the following is the correct simplified form of $$\frac{x^2$ - 9}{x - 3}$$ for $$x 
eq 3$$?

Accepted Answer

$$x + 3$$

Question 13

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

Accepted Answer

$$f(-2) = 15$$

Question 14

A company models its profit $$P in $$thousands of dollars by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). How many units should be sold to maximize profit?

Accepted Answer

$$x = 3$$

Question 15

Which of the following is the correct interval notation for the range of $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 16

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

Accepted Answer

$$(f \circ g)(x) = (x-2)^2$

Question 17

Which of the following is the correct solution set for $$x^2 + 6x + 9 = 0$?

Accepted Answer

$$x = -3$$

Question 18

A rectangular garden has an area of $$48$$ square meters. If the length is $$l$$ meters and the width is $$w$$ meters, and the length is $$4$$ meters longer than the width, what are the dimensions of the garden?

Accepted Answer

Width $$w = 6 m$$, Length $$l = 10 m$$

Question 19

Which of the following is the correct vertex form of the quadratic $$y = x^2$ + 4x + 1$$?

Accepted Answer

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

Exam 4 Study Guide: Polynomial and Rational Functions, Quadratic Equations, and Related Topics

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