Question 1

Given the quadratic function $$f(x) = -4(x - 7)^2$ + 11$$, what is the vertex of the parabola?

Accepted Answer

$$(7, 11)$$

Question 2

For the function $$f(x) = x^2$ + 3x - 2$$, does the parabola open upwards or downwards?

Accepted Answer

Upwards

Question 3

If the graph of a quadratic function does not intersect the $$x-$$axis, what can you say about its discriminant?

Accepted Answer

The discriminant is negative

Question 4

Solve for $$x$$: $$4x^2 = 108$

Accepted Answer

$$x = 3 or$$ $$x = -3$$

Question 5

A company produces brake rotors. The total revenue function is $$R(x) = 4x - 20$$ and the total cost function is $$C(x) = 0.002x^2$ + 0.8x + 50. $$What is the profit function $$P(x)$$?

Accepted Answer

$$P(x) = 4x - 20 - (0.002x^2$ + 0.8x + 50)$$

Question 6

Given the function $$f(x) = 3x - 2$$ for $$x \u003c -1$$ and $$f(x) = 4 - x^2$ for x$$ \geq -1$$, which of the following describes the graph at x = -1$?

Accepted Answer

There is a jump discontinuity at $$x = -1$$

Question 7

If $$f(x) = 0$$ has no real solutions for a quadratic function, what does this imply about the graph?

Accepted Answer

The graph does not intersect the $$x-$$axis

Question 8

A ball is thrown and its height is modeled by $$h(t) = -16t^2$ + 32t + 5. $$What is the maximum height of the ball?

Accepted Answer

$$37$$ feet

Question 9

For the quadratic function $$y = 4.97x^2$ - 0.126x$$, is the graph concave up or down?

Accepted Answer

Concave up

Question 10

The cost to cater a dinner meeting is given by $$C(x) = \begin{cases} 300 & 	ext{if } 0  30 \end{cases}$$, where $$x is $$the number of meals served. What is $$C(60)$$?

Accepted Answer

$$660$$

Question 11

Given the quadratic function $$f(x) = ax^2$ + bx + c$$, what is the formula for the axis of symmetry?

Accepted Answer

$$x = -\frac{b}{2a}$$

Question 12

If the range of a quadratic function is $$y \geq -3$$, what does this tell you about the vertex?

Accepted Answer

The vertex is at the minimum point $$(-3)$$

Question 13

A company’s profit function is $$P(x) = -0.002x^2$ + 3.2x - 70. $$How many units must be produced and sold to maximize profit?

Accepted Answer

$$x = 800$$

Question 14

For the quadratic equation $$x^2 + 6x + 9 = 0$, how many real solutions are there?

Accepted Answer

One real solution

Question 15

If the axis of symmetry of a parabola is $$x = 2$$, which of the following could be the equation of the parabola?

Accepted Answer

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

Question 16

A quadratic function models the height of a ball: $$h(t) = -16t^2$ + 32t + 5. $$When does the ball hit the ground?

Accepted Answer

$$t = 2.21$$ seconds

Question 17

If the cost function for a company is $$C(x) = 0.002x^2$ + 0.8x + 50$$ and the revenue function is $$R(x) = 4x - 20$$, what is the break-even point?

Accepted Answer

$$x \approx 15$$ units

Question 18

For the function $$y = 4.97x^2$ - 0.126x$$, what percent is projected for 2026 if $$x is $$the number of years after 2000?

Accepted Answer

$$y = 4.97(26)^2$ - 0.126(26) \approx 3357.6$$

College Algebra: Quadratic Functions, Equations, and Applications Study Guide

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