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?

Accepted Answer

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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