Q: What is the quadratic formula for solving $$ax^2 + bx + c = 0$?

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

Q: The number of fatal crashes per 100 million miles driven, $$F$$, for drivers of age $$x is $$modeled by $$F = 0.013x^2$ - 1.19x + 28.24. $$What age groups are expected to be in 3 fatal crashes per 100 million miles driven?

$$x \\approx 7$$ and $$x \\approx 31$$

Q: If $$x^2 + bx$ is a binomial, what must be added to create a perfect square trinomial?

$$\\left(\\frac{b}{2}\\$$right)^2$$

Question 1

Which of the following best defines a quadratic equation?

Accepted Answer

An equation where the highest power of the variable is 2.

Question 2

What is the Zero-Product Principle used for when solving quadratic equations?

Accepted Answer

To set each factor equal to zero when a product equals zero.

Question 3

Solve the equation $$3x^2 + 12x = 0$ by factoring. What are the solutions?

Accepted Answer

$$x = 0$$ and $$x = -4$$

Question 4

Which term should be added to $$x^2 + 6x$ to create a perfect square trinomial?

Accepted Answer

$$9$$

Question 5

Solve $$3x^2 - 21 = 0$ using the square root method. What are the solutions?

Accepted Answer

$$x = \pm \sqrt{7}$$

Question 6

What is the quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

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

Question 7

What does the discriminant $$b^2 - 4ac$ tell you about the solutions of a quadratic equation?

Accepted Answer

It tells you the number and type of solutions.

Question 8

For the equation $$x^2 - 2x + 1 = 0$, what is the value of the discriminant and what does it indicate?

Accepted Answer

Discriminant is $$0$$, indicating one real solution.

Question 9

Solve $$x^2 - 6x - 11 = 0$ by completing the square. What are the solutions?

Accepted Answer

$$x = 3 \pm \sqrt{20}$$

Question 10

A quadratic function models a woman’s normal systolic blood pressure: $$P_A = 0.01A^2$ + 0.05A + 107. $$What is the age, to the nearest year, of a woman whose normal systolic blood pressure is 115 mmHg?

Accepted Answer

$$A = 27$$

Question 11

The number of fatal crashes per 100 million miles driven, $$F$$, for drivers of age $$x is $$modeled by $$F = 0.013x^2$ - 1.19x + 28.24. $$What age groups are expected to be in 3 fatal crashes per 100 million miles driven?

Accepted Answer

$$x \approx 7$$ and $$x \approx 31$$

Question 12

Which method is most appropriate for solving $$x^2 = 8x - 15$?

Accepted Answer

Factoring

Question 13

If the discriminant of a quadratic equation is negative, what can you conclude?

Accepted Answer

There are two complex solutions.

Question 14

Solve $$x^2 - 4x - 5 = 0$ using the quadratic formula. What are the solutions?

Accepted Answer

$$x = 5$$ and $$x = -1$$

Question 15

What is the axis of symmetry for the graph of $$y = ax^2$ + bx + c$$?

Accepted Answer

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

Question 16

Which of the following is NOT a method for solving quadratic equations?

Accepted Answer

Using the cube root method

Question 17

If $$x^2 + bx$ is a binomial, what must be added to create a perfect square trinomial?

Accepted Answer

$$\left(\frac{b}{2}\$$right)^2$$

Question 18

What is the solution to $$x^2 + 4x - 1 = 0$ by completing the square?

Accepted Answer

$$x = -2 \pm \sqrt{5}$$

Question 19

Which real-world scenario can be modeled by a quadratic equation?

Accepted Answer

The height of a projectile as a function of time.

Step-by-Step Guidance for Quadratic Equations (Algebra & Trigonometry)

Guida di studio - Domande di pratica

Study guide - Flashcard