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?

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 $a > 0$, 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?

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

Study Guide - Practice Questions

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