Question 1

Which of the following is the axis of symmetry for the quadratic equation $$x^2 + 10x + 24 = 0$?

Accepted Answer

$$x = -5$$

Question 2

What is the vertex of the parabola given by $$x^2 + 10x + 24$?

Accepted Answer

$$(-5, -1)$$

Question 3

What is the domain of any quadratic function, such as $$y = -3x^2$ - 6x$$?

Accepted Answer

$$x \in (-\infty, \infty)$$

Question 4

For the quadratic $$y = -3x^2$ - 6x$$, what is the range of the function?

Accepted Answer

$$y \in (-\infty, 3)$$

Question 5

Solve the quadratic equation $$x^2 - 11x + 18 = 0$ by factoring. What are the solutions?

Accepted Answer

$$x = 9$$ and $$x = 2$$

Question 6

A biologist models the population of a species with the quadratic $$2x^2 - 32x + 128 = 0$. What are the possible values of x$ (time in months) when the population is zero?

Accepted Answer

$$x = 8 ($$double root)

Question 7

Solve $$8x^2 + 10x = 0$ by factoring. What are the solutions?

Accepted Answer

$$x = 0$$ and $$x = -\frac{10}{8}$$

Question 8

Which of the following best describes the direction in which the parabola $$y = -3x^2$ - 6x$$ opens?

Accepted Answer

Downward

Question 9

A projectile is launched and its height is modeled by $$x^2 + 10x + 24$. What is the minimum value of the height?

Accepted Answer

$$-1$$

Question 10

Given the quadratic $$7x^2 - 19x - 6 = 0$, which of the following is the correct factorization?

Accepted Answer

$$(7x + 2)(x - 3)$$

Question 11

A company models its profit with $$x^2 - 11x + 18$. If the profit is zero, what are the break-even points?

Accepted Answer

$$x = 9$$ and $$x = 2$$

Question 12

Which of the following is the correct method to find the vertex of $$y = ax^2$ + bx + c$$?

Accepted Answer

Use $$x = -\frac{b}{2a}$$ and substitute into the equation

Question 13

For the quadratic $$2x^2 - 32x + 128 = 0$, what is the axis of symmetry?

Accepted Answer

$$x = 8$$

Question 14

If a quadratic equation has a positive leading coefficient, what is the direction of the parabola?

Accepted Answer

Upward

Question 15

A medical researcher models the spread of a virus with $$8x^2 + 10x = 0$. What is the significance of the solution x = 0$?

Accepted Answer

The initial time when the spread starts

Question 16

Which of the following statements about the range of $$y = x^2$ + 10x + 24 is $$correct?

Accepted Answer

$$y \in [-1, \infty)$$

Question 17

A quadratic equation $$ax^2 + bx + c = 0$ is solved by factoring. Which step comes first?

Accepted Answer

Set the equation equal to zero

Question 18

If the roots of a quadratic equation are real and equal, what does this indicate about the graph?

Accepted Answer

The parabola touches the x-axis at one point

Question 19

Which of the following is a real-world scenario that can be modeled by a quadratic equation?

Accepted Answer

The height of a thrown ball over time

Quadratic Equations: Graphing, Key Features, and Factoring Guidance

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