Features of Graphs
Features from Equations
Standard Form
Word Problems
Vertex Form
100
What is the y-intercept?
y=4 or (0, 4)
100
What is the y-intercept?
y = x2 + 14x + 40
y=40
(0, 40)
100
(x + 4)(x + 6)
x2 + 10x + 24
100
In the equation: y = -16x2 + 45x + 100
what does the number -16 represent?
The effect of gravity.
100
What is the vertex in the equation: y = (x - 3)2 + 6
(3, 6)
200
What are the x-intercepts (aka - zeros)?
x=-1 and x=3
(-1,0) & (3,0)
200
What are the zeros (aka: x-intercepts)?
y = (x - 5)(x - 5)
x=5
(5,0)
200
(x - 6)2
(x - 6)(x - 6)
x2 - 12x + 36
200
In the equation: y = -16x2 + 45x + 100
what does the number 45 represent?
The speed of the object.
200
What is the vertex in the equation: y = (x + 4)2 + 6
(-4, 6)
300
What is the vertex of the graph?
Is it a minimum or maximum?
(-2, -3)
Minimum
300
What are the x-intercepts?
y = (x - 1)(x - 7)
(x - 1)(x - 7)
x=1 and x=7
300
What graph feature is easiest to find given standard form ax2 + bx + c?
What letter is it represented by?
y-intercept
"c"
300
In the equation: y = -16x2 + 45x + 100
what does the number 100 represent?
100 feet
300
Translate the equation down 4.
y = (x - 3)2 + 6
y = (x - 3)2 + 2
400
What are the zeros?
x=6 and x=8
(6,0) & (8,0)
400
What is the vertex? Is it a minimum or maximum?
y = - (x - 5)2 + 8
Vertex: (5, 8)
Maximum because the "a" is negative making the graph a FROWN.
400
(3x + 4)2 - 2x
9x2 + 22x + 16
400
When does the object hit the ground given the equation below?
y = 16(x+5)(2-x)
x = 2 seconds
400
Does it open down or up?
Is it a minimum or maximum?
y = (x - 3)2 + 6
Up
Minimum
500
What is the vertex? Is it a max or min?
What are the zeros?
What is the y-intercept?
Vertex: (1.5, 4.5) Maximum
Zeros: x=0 and x=3
Y-Intercept: y=0
500
What are the x-intercepts?
What is the vertex?
y = (x + 3)(x + 5)
(x+3)(x+5)
x-intercepts: x = -3 & x = -5
vertex: (-4 ~ because it is in between -3 and -5
, -1) ~ because that's what you get when you substitute -4 into the equation.
500
Distribute & Combine Like Terms:
(3x + 2)2 - 2x + 5
(3x + 2)(3x + 2) -2x + 5
9x2 + 6x + 6x + 4 - 2x + 5
9x2 + 10x + 9
500
What is the initial height of the object given the equation below?
y = 16(x+5)(2-x)
160 feet
500
Translate the equation left 2 and down 5.
y = (x - 3)2 + 6
y = (x - 1)2 + 1