IM A2A U2 | Check Your Readiness

We can calculate the volume V of a rectangular prism using V = ℓwh, where ℓ is the length, w is the width, and h is the height of the prism. Suppose that a prism has a volume of 200 cm³ and ℓ = 2w.

Rewrite the volume formula by making substitutions for V and ℓ.

• 200 = 2w²h

• 200 = 4wh

• 200 = 2wh

• 200 = 4w²h

We can calculate the volume V of a rectangular prism using V = ℓwh, where ℓ is the length, w is the width, and h is the height of the prism. Suppose that a prism has a volume of 200 cm³ and ℓ = 2w.

When rewritten, we would have 200 = 2w²h

Rewrite the equation as h in terms of w. (Turn it into h = something.)

• h = 100/w²

• h = 200/w²

• h = 50/w²

• h = 25/w²

Select all expressions that are equivalent to x² - 4x - 32.

• (x + 4)(x - 8)

• (x + 8)(x - 4)

• (x - 16)(x + 2)

• (x + 2)(x - 16)

• (x - 8)(x + 4)

Select all solutions to the equation (2x - 4)(x + 5) = 0.

• x = -5

• x = 1/2

• x = 2

• x = -1/2

• x = -2

Show that (3x - 1)(x + 5) is equivalent to 3x² + 14x - 5

The height of a softball, in feet, is modeled by the function h given by h(t) = 3 + 5t - 16t², where t is the time, in seconds, after the softball is hit.

A graph of the function is shown.

About when does the softball reach its maximum height?

The height of a softball, in feet, is modeled by the function h given by h(t) = 3 + 5t - 16t², where t is the time, in seconds, after the softball is hit.

A graph of the function is shown.

About how high is the maximum height of the softball?

The height of a softball, in feet, is modeled by the function h given by h(t) = 3 + 5t - 16t², where t is the time, in seconds, after the softball is hit.

A graph of the function is shown.

About when does the ball hit the ground?

Here is a graph that represents a quadratic function. Which equation could define this function?

• y = (x - 2)(x + 3)

• y = (x - 2)(x - 3)

• y = (x + 2)(x + 3)

• y = (x + 2)(x - 3)

Solve the equation 2x² - 7x - 15 = 0. Explain or show your work.