Features of Graphs
Factored Form
Features from Equations
Standard Form
Find the Error
100
What is the y-intercept?
y=4 or (0, 4)
100
Factor:
x2 + 10x + 25
(x+5)(x+5)
100
What is the y-intercept?
y = x2 + 14x + 40
y=40
(0, 40)
100
Distribute:
(x + 4)(x + 6)
x2 + 10x + 24
100
(x - 3)(x + 5) = 0
x = 3 & x = 5
It should be x = -5.
You always do the opposite of what's in ( ).
200
What are the x-intercepts (aka - zeros)?
x=-1 and x=3
(-1,0) & (3,0)
200
Factor:
x2 - 3x - 10
(x-5)(x+2)
200
What are the zeros (aka: x-intercepts)?
y = (x - 5)(x - 5)
x=5
(5,0)
200
Distribute:
(x - 6)2
(x - 6)(x - 6)
x2 - 12x + 36
200
y = (x - 2)2 - 6
The vertex is (-2, -6) and it is a minimum.
You need to do the opposite of what's in ( ).
So the vertex is (2, -6) and it is a minimum because the "a" value is positive.
300
What is the vertex of the graph?
Is it a minimum or maximum?
(-2, -3)
Minimum
300
Factor:
x2 - 100
(x+10)(x-10)
300
What are the x-intercepts?
y = x2 - 8x + 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
Factor: x2 + 8x - 20
(x + 2)(x - 10)
2 + -10 = -8 but we want +8
so you need to switch the numbers
(x + 10)(x - 2)
400
What are the zeros?
x=6 and x=8
(6,0) & (8,0)
400
Factor:
x2 - 20x
x(x-20)
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
You throw a ball off the top of the school. It follows the equation y = -16x2 + 10x + 72.
What is the height of the school?
72 feet
400
x2 + 5x - 36 = -22
(x + 9)(x - 4) = -22
x = -9 and x = 4
You need to use ZPP (zero product property).
So ADD 22 to get it = 0.
x2 + 5x - 14 = 0
then factor to (x + 7)(x - 2) = 0
x = -7 and x = 2
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
Factor:
4x2 - 25
(2x+5)(2x-5)
500
What are the x-intercepts?
What is the vertex?
y = x2 + 8x + 15
(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
x2 - 16x and x2 - 16
both factor to
(x - 4)(x + 4)
x2 - 16 factors to (x - 4)(x + 4)
but x2 - 16x factors to x(x - 16)