Question 1

Which of the following equations is a quadratic equation?

Accepted Answer

$$2x^2 - 5x + 3 = 0$

Question 2

A ball is thrown upward from the ground with an initial velocity. Its height $$h (in $$meters) after $$t$$ seconds is given by $$h = -4.9t^2$ + 20t. $$When does the ball hit the ground again?

Accepted Answer

$$t = 0 or$$ $$t \approx 4.08$$

Question 3

What is the discriminant of the quadratic equation $$3x^2 - 6x + 2 = 0$ and how many real solutions does it have?

Accepted Answer

Discriminant is $$(-6)^2 - 4$$ \cdot 3 \cdot 2 = 36 - 24 = 12$$, so there are 2 real solutions.

Question 4

Solve the equation $$x^2 - 9 = 0$.

Accepted Answer

$$x = 3 or$$ $$x = -3$$

Question 5

Which of the following best describes the solutions to $$x^2 + 4 = 0$?

Accepted Answer

Two imaginary solutions: $$x = 2i$$ and $$x = -2i$$

Question 6

A chemical reaction's rate is modeled by $$r = t^2$ - 6t + 8. At $$what time(s) $$t is $$the rate zero?

Accepted Answer

$$t = 2 or$$ $$t = 4$$

Question 7

Which method is most appropriate to solve $$x^2 - x - 12 = 0$?

Accepted Answer

Factoring

Question 8

Solve for $$x$$: $$2x^2 - 1 = 9$

Accepted Answer

$$x = 2 or$$ $$x = -2$$

Question 9

A medical dosage is modeled by $$d = x^2$ - 4x + 4. $$What is the minimum dosage, and at what value of $$x$$ does it occur?

Accepted Answer

Minimum is $$0 at$$ $$x = 2$$

Question 10

Which of the following statements about the discriminant is correct?

Accepted Answer

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

Question 11

Solve for $$x$$ using the quadratic formula: $$x^2 = 4x - 9$

Accepted Answer

$$x = 2 + \sqrt{13} or$$ $$x = 2 - \sqrt{13}$$

Question 12

Which step is NOT part of the process of completing the square for $$ax^2 + bx + c = 0$?

Accepted Answer

Multiply both sides by the leading coefficient

Question 13

A projectile's height is modeled by $$h = -16t^2$ + 32t + 48. $$When does it reach the ground?

Accepted Answer

$$t = -1 or$$ $$t = 3$$

Question 14

Given $$2(x-4)^2 - 16 = 0$, what are the solutions for x$?

Accepted Answer

$$x = 4 + 2\sqrt{2} or$$ $$x = 4 - 2\sqrt{2}$$

Question 15

If a quadratic equation has a discriminant of zero, what can you conclude about its solutions?

Accepted Answer

There is exactly one real solution.

Question 16

Solve by completing the square: $$x^2 + 6x + 5 = 0$

Accepted Answer

$$x = -1 or$$ $$x = -5$$

Question 17

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

Accepted Answer

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

Question 18

A quadratic equation models the profit $$P (in $$dollars) for a company: $$P = -2x^2$ + 8x + 10. $$What is the maximum profit, and at what value of $$x$$ does it occur?

Accepted Answer

Maximum profit is $$26 at$$ $$x = 2$$

Question 19

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

Accepted Answer

Factoring

Quadratic Equations: Methods of Solution and the Discriminant

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