Question 1

Which of the following equations is a quadratic equation in standard form?

Accepted Answer

$$x^2 + 3x - 7 = 0$

Question 2

A quadratic equation $$x^2 - 5x + 6 = 0$ is solved by factoring. What are the solutions?

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 3

Which principle allows us to set each factor equal to zero when solving $$x^2 - 4x = 0$ by factoring?

Accepted Answer

Zero-Product Principle

Question 4

Solve the equation $$x^2 = 49$ using the square root property.

Accepted Answer

$$x = 7$$ and $$x = -7$$

Question 5

What value must be added to $$x^2 + 6x$ to complete the square?

Accepted Answer

$$9$$

Question 6

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

Accepted Answer

$$x = -2 \pm \sqrt{3}$$

Question 7

Given the quadratic equation $$2x^2 - 3x + 5 = 0$, what is the discriminant and what does it indicate about the solutions?

Accepted Answer

Discriminant is $$(-3)^2 - 4$$ \cdot 2 \cdot 5 = 9 - 40 = -31$$, so there are two imaginary solutions.

Question 8

A woman’s normal systolic blood pressure is modeled by $$P = 0.066A^2$ + 0.47A + 50$$, where $$A is $$age. If $$P = 115$$, what is the approximate age $$A (to $$the nearest year)?

Accepted Answer

$$A \approx 26$$

Question 9

Which method is most efficient for solving $$x^2 - 16 = 0$?

Accepted Answer

Square Root Property

Question 10

If the discriminant of a quadratic equation is zero, what can be said about its solutions?

Accepted Answer

There is one real (repeated) solution.

Question 11

Solve $$3x^2 + 6x = 0$ by factoring. What are the solutions?

Accepted Answer

$$x = 0$$ and $$x = -2$$

Question 12

A right triangle has legs of length $$a = 9$$ and $$b = 12. $$What is the length of the hypotenuse $$c$$?

Accepted Answer

$$c = 15$$

Question 13

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

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

Question 14

Which scenario best illustrates the use of completing the square in a real-world context?

Accepted Answer

Calculating the minimum height of a projectile given its quadratic path equation.

Question 15

If $$x^2 + 2x + 1 = 0$, what are the solutions?

Accepted Answer

$$x = -1 ($$repeated solution)

Question 16

A TV screen has a width of 24 inches and a height of 18 inches. What is the diagonal size of the screen?

Accepted Answer

$$\sqrt{24^2$ + 18^2$} = 30$$ inches

Question 17

Which of the following quadratic equations has two unequal real solutions?

Accepted Answer

$$x^2 - 2x - 3 = 0$

Question 18

What is the most efficient method to solve $$x^2 + 8x + 16 = 0$?

Accepted Answer

Factoring

Question 19

A chemical reaction is modeled by $$t^2 - 6t + 9 = 0$, where t$ is time in seconds. How long does the reaction take to complete?

Accepted Answer

$$t = 3$$ seconds

Question 20

Which of the following statements about the discriminant is correct?

Accepted Answer

If $$b^2 - 4ac$$ \u003c 0$$, the equation has two imaginary solutions.

Quadratic Equations: Methods, Properties, and Applications

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