Question 1

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

Accepted Answer

$$f(x) = ax^2$ + bx + c$$

Question 2

Given the quadratic function $$f(x) = 2x^2$ - 8x + 3$$, what is the x-coordinate of the vertex?

Accepted Answer

$$x = 2$$

Question 3

A company’s revenue and cost functions are $$R(x) = x(200 - 4x)$$ and $$C(x) = 160 + 20x$$, where $$x is in $$millions. How many components must be sold to break even? (Round to the nearest million.)

Accepted Answer

$$x = 49$$

Question 4

Which of the following best describes the axis of symmetry for the quadratic function $$f(x) = a(x - h)^2$ + k$$?

Accepted Answer

$$x = h$$

Question 5

For the quadratic function $$f(x) = -x^2$ + 18x + 19$$, what is the maximum value of the function?

Accepted Answer

$$k = 100$$

Question 6

Given $$C(x) = 0.01x^2$ - 20x + 25,000$$ for $$1000 \leq x \leq 3500$$, what is the minimum cost to build a house, and at what square footage does it occur?

Accepted Answer

Question 7

Which of the following functions is quadratic?

Accepted Answer

$$y = 3x^2$ - 2x + 5$$

Question 8

If a quadratic function opens upwards, which of the following is true?

Accepted Answer

The coefficient $$a is $$positive and the vertex is a minimum.

Question 9

What is the quadratic formula used to solve $$ax^2 + bx + c = 0$?

Accepted Answer

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

Question 10

A company’s profit function is $$P(x) = R(x) - C(x)$$, where $$R(x) = x(200 - 4x)$$ and $$C(x) = 160 + 20x. $$What is the maximum profit, and how many components must be sold to achieve it?

Accepted Answer

Maximum profit is $$400$$ million at $$x = 25$$ million

Question 11

Which of the following statements about the domain and range of a quadratic function $$f(x) = ax^2$ + bx + c is $$correct?

Accepted Answer

Domain is all real numbers; range depends on the direction the parabola opens.

Question 12

If the minimum value of a quadratic function $$f(x) = ax^2$ + bx + c is$$ $$k$$ and $$a \u003e 0$$, where does this minimum occur?

Accepted Answer

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

Question 13

Given $$f(x) = 3x^2$ - 2x + 5$$, what is the axis of symmetry?

Accepted Answer

$$x = \frac{1}{3}$$

Question 14

A builder uses the cost function $$C(x) = 0.01x^2$ - 20x + 25,000$$ for $$1000 \leq x \leq 3500. $$What is the cost to build a 1500 square foot house?

Accepted Answer

Question 15

Which of the following is NOT a quadratic function?

Accepted Answer

$$f(x) = 4x - 3(x + 2) - x$$

Question 16

If a quadratic function has no real x-intercepts, what can you conclude about its discriminant $$b^2 - 4ac$?

Accepted Answer

The discriminant is negative.

Question 17

Given $$f(x) = x^2$ + 2x - 4$$, what are the x-intercepts?

Accepted Answer

$$x = -1 \pm \sqrt{5}$$

Question 18

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

$$h = 21.9$$ meters

Question 19

Which of the following real-world scenarios can be modeled by a quadratic function?

Accepted Answer

The area of a rectangular garden with a fixed perimeter.

Quadratic Functions and Applications in College Algebra

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