Q: 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?

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

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

$b^2 - 4ac < 0$

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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