Question 1

Which of the following is the correct quadratic formula for solving $ax^2 + bx + c = 0$?

Accepted Answer

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Question 2

A ball is thrown upward from a height of 60 feet above the ground. Its height after $t$ seconds is given by $h(t) = -16t^2 + 60$. How long will it take for the ball to hit the ground?

Accepted Answer

$t = \frac{\sqrt{60}}{4}$

Question 3

Given the function $f(x) = 3x^2 - 12x + 9$, what are the $x$-intercepts?

Question 4

Which of the following describes the transformation for $y = f(x - 3)$ compared to $y = f(x)$?

Accepted Answer

Shift 3 units to the right

Question 5

If the discriminant $D$ of a quadratic equation $ax^2 + bx + c = 0$ is negative, what does this indicate about the solutions?

Accepted Answer

There are two complex solutions

Question 6

Find the vertex of the parabola $y = 2x^2 + 12x - 1$.

Accepted Answer

$(-3, -19)$

Question 7

Which of the following is the factored form of $3x^2 - 11x - 6$?

Accepted Answer

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

Question 8

A missile is launched upward from the ground. Its height in feet after $t$ seconds is given by $h(t) = -16t^2 + 250t + 150$. How long will it take to reach a height of 800 feet? (Round to the nearest tenth)

Accepted Answer

$t \approx 6.0$

Question 9

Which of the following is the correct vertex form of a quadratic function?

Accepted Answer

$y = a(x - h)^2 + k$

Question 10

Given $f(x) = x^2$ and $g(x) = x + 5$, what is $f(g(2))$?

Accepted Answer

$25$

Question 11

Which of the following is true about the graph of $y = -2x^2 + 4x - 3$?

Accepted Answer

It opens downward and has a maximum

Question 12

If $f(x) = x^2$ and $g(x) = x + 3$, which function is the composition $f(g(x))$?

Accepted Answer

$f(g(x)) = (x + 3)^2$

Question 13

Which of the following is the correct method to solve $x^2 = 5$?

Accepted Answer

$x = \pm \sqrt{5}$

Question 14

The points $(1,2)$, $(4,6)$, and $(8,2)$ lie on the graph of $y = f(x)$. Which of the following points will be on the graph of $y = f(x - 3)$?

Accepted Answer

$(4,2)$, $(7,6)$, $(11,2)$

Question 15

Which of the following is the correct way to complete the square for $x^2 + 4x + 5$?

Accepted Answer

$(x + 2)^2 + 1$

Question 16

If $f(x) = x^2$ and $g(x) = 2x$, what is $f(g(3))$?

Accepted Answer

$36$

Question 17

Which of the following is the correct standard form of a quadratic function?

Accepted Answer

$y = ax^2 + bx + c$

Question 18

Given the equation $x^2 - 5x + 6 = 0$, what are the solutions?

Accepted Answer

$x = 2$ 	ext{ and } x = 3$

Question 19

Which of the following statements is true about the function $f(x) = \sqrt{x}$?

Accepted Answer

The domain is $x \geq 0$

College Algebra: Quadratic Functions, Graphs, and Problem Solving

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