Week 9 Quiz

What is the vertex of the parabola f(x) = (x + 3)² − 5?

Select one.

• (3, −5)
• (−3, −5)
• (−3, 5)
• (3, 5)

Use the vertex formula h = −b ⁄ (2a) to find the vertex of the week's parabola f(x) = x² − 6x + 5.

Select one.

• (−3, 32)
• (0, 5)
• (3, −4)
• (6, 5)

The parabola f(x) = −x² + 4x + 1 has a = −1, b = 4, and c = 1. Which statement gives its vertex and says what kind of value the vertex is?

Select one.

• (2, 5), a maximum value
• (2, 5), a minimum value
• (−2, −11), a maximum value
• (2, 13), a maximum value

The parabola f(x) = (x − 2)² + 3 expands to x² − 4x + 7. How many x-intercepts does it have?

Select one.

• Two, because the discriminant 16 + 28 = 44 is positive
• One, because the vertex (2, 3) is a single point
• Two, because a = 1 is positive
• None, because the discriminant 16 − 28 = −12 is negative

What is the y-intercept of the week's parabola f(x) = x² − 6x + 5?

Select one.

• (0, −4)
• (0, 5)
• (0, 1)
• (5, 0)

The week's parabola f(x) = x² − 6x + 5 has vertex (3, −4) and a = 1. What is its range?

Select one.

• [−4, ∞)
• (−∞, −4]
• [3, ∞)
• [5, ∞)

For the week's parabola, f(2) = −3, and the axis of symmetry is x = 3. Which other input x gives f(x) = −3?

Select one.

• −2
• 3
• 4
• 8

Which is the standard form of f(x) = 2(x − 1)² − 3?

Select one.

• 2x² − 5
• 4x² − 8x + 1
• 2x² − 2x − 1
• 2x² − 4x − 1

A launched object's height in feet t seconds after launch is h(t) = −16t² + 64t + 80. When does it reach its greatest height, and how high is that?

Select one.

• After 2 seconds, at 144 feet
• After 5 seconds, at 0 feet
• At the moment of launch, at a height of 80 feet
• After 2 seconds, at 80 feet

A rectangular garden is surrounded by 40 feet of fencing, so its area is A(w) = w(20 − w) = −w² + 20w square feet for a width of w feet. Which width gives the largest area, and what is that area?

Select one.

• A width of 20 feet, for 400 square feet
• A width of 10 feet, for 100 square feet
• A width of 12 feet, for 96 square feet
• A width of 5 feet, for an area of 75 square feet