2324QuadGraphs

Question 1

What can you learn about the graph of a parabola by looking at the equation?

Answer 1

ax² + bx + c = 0

If a is positive, it points up. (end behavior)

You can find the vertex.

You can find the y-intercept. (at most 1)

You can find the x-intercepts. (at most 2)

Question 2

Describe the graph for

x² - 4x +4

Answer 2

(1) The ends point up
(2) It sits on the x-axis at x = 2

(x - 2)² ^{(it’s a perfect square)}

So its lowest point (vertex) is (2,0)

(3) y-intercept is 4

Question 3

What is the formula to find the vertex of a parabola?

Answer 3

y = (x - m)² + n

vertex = (m,n)

Question 4

Describe the graph of:

y = x² + 6x + 5

Answer 4

(1) The ends face up.
(2) The y-intercept is 5
(3) (x² + 6x + 9) + 5 - 9 = 0

(x + 3)² - 4 = 0

vertex = -3,-4

(4) (x + 5)(x + 1)

x-intercepts = -5 and -1

Question 5

A box has a volume of 280 cm³.

Its dimensions are

4 cm*x *(x + 3)

What are its dimensions?

Answer 5

4x² + 12x = 280

:: x² + 3x = 70

(x² + 3x + ⁹/₄) -⁹/₄ = 70

(x + ³/₂)² = 72 ¼

x + ³/₂ = ±√72.25

x = -³/₂ + 8.5 (The answer must be positive)

x = 7

The box is 4*7*10

Question 6

A can of paint will cover 600 square feet.

What is the radius of the largest circle 3 cans of paint will cover?

Answer 6

πr² = 1800

r² = 572.96

r ≈ 23.94 ft.

Question 7

A rocket is fired in the air.

after t seconds it is at

height = -16t² + 192t

What is its maximum height and when will it reach it?

Answer 7

h = -16t(t + 12)

The height is 0 at 0 and 12.

The highest point will be at t = 6

= 576 ft. (the vertex of the parabola)