Pd 6 Quadratics Quiz

A ball was thrown upward in the air. The height, in feet, of the ball above the ground t seconds after being thrown can be determined by the expression −16𝑡² + 40𝑡 + 3. What is the meaning of 3 in the expression? Select the correct answer.

• The ball takes 3 seconds to reach its maximum height.

• The ball takes 3 seconds to reach the ground.

• The ball was thrown from a height of 3 feet.

• The ball reaches a maximum height of 3 feet.

A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds.

For which interval is the ball’s height always decreasing?

• 0 ≤ 𝑥 ≤ 2.5

• 0 < 𝑥 < 5.5

• 2.5 < 𝑥 < 5.5

• 𝑥 ≥ 2

How many real solutions does

x² - 4x + 4 = 0 have?

• 0

• 1

• 2

How many real solutions does

3x² - 2x = 10x - 12

^have?

• 0

• 2

• 1

Which value of c completes the square in the expression

x² + 14x + c?

• -49

• -7

• 7

• 49

Solve  $x^2$   + 12x + 25 = 17 by completing the square. Select all the possible solutions

• −6 + √ 7 

• −6 + 2√ 7

• 6 − 2√ 7 

• −6 − √ 7 

• −6 − 2√ 7 

Which equation has no real solutions?

• −2x² = −168

• 4x² + 76 = 32

• 25x² = 1

• 43 − x² = 12

What are the solutions of the equation  $4x^2$   − 2x + 2 − 3x − x2 = 0?

•  1 and 2 

• 1 and 2/3

• −1 and −2

• −1 and −2/3

Solve the equation x² + 9x = 36 by factoring.

(if there is more than 1 answer, put the word "and" between them)

Write an expression for the product  $\left(\sqrt{6x}\right)\left(\sqrt{15x^3}\right)$  
without a perfect square factor in the radicand.

•  $3x\sqrt{10}$  

•  $\sqrt{45x^4}$  

•  $3x^2\sqrt{10}$  

•  $3\sqrt{15x^3}$