2324QuadGraphs Flashcards
What can you learn about the graph of a parabola by looking at the equation?
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)
Describe the graph for
x² - 4x +4
(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
What is the formula to find the vertex of a parabola?
y = (x - m)² + n
vertex = (m,n)
Describe the graph of:
y = x² + 6x + 5
(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
A box has a volume of 280 cm³.
Its dimensions are
4 cm*x *(x + 3)
What are its dimensions?
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
A can of paint will cover 600 square feet.
What is the radius of the largest circle 3 cans of paint will cover?
πr² = 1800
r² = 572.96
r ≈ 23.94 ft.
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?
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)