Graphing Quadratics
Questions to consider:
1. What are some points of interest that we can use when graphing quadratics?
2. What are the different forms of a quadratic and what pieces of information do
they give us?
What is the y value of any point on the x-axis?
What is the x value of any point on the y-axis?
This means, if we want to find the x-intercepts, then we should set y=0. If we want
to find the y-intercepts, then we should set x=0.
There are three forms of a quadratic that we are going to talk about:
1. Standard Form: 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
−𝑏
 The x-value of the vertex is
 Axis of symmetry is 𝑥 =
 This is easily factorable
−𝑏
2𝑎
2𝑎
2. Vertex Form: 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘
 vertex is (h, k) – remember bad dog
 axis of symmetry is 𝑥 = ℎ
3. Intercept Form: 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞)
 x-intercepts are 𝑝 and 𝑞
 axis is halfway between 𝑝 and 𝑞
In any form, if 𝑎 > 0, then the graph opens ______________
If 𝑎 < 0, then the graph opens ___________
The graph gets ________________ as |𝑎| gets larger.
The graph gets ________________ as |𝑎| gets smaller.
Some good starting points
𝑏
 vertex – probably using −
2𝑎
 does it open up or down?
 x-intercepts
 y-intercepts
 May need to plug in some points – the good ol’ table method
Lets try some:
𝑦 = 2𝑥 2 − 8𝑥 + 6
Vertex
x-int
y-int
Up/down?
You try one:
𝑦 = 𝑥 2 − 𝑥 − 12
Vertex
x-int
y-int
Up/down?
Let’s try one in vertex form:
1
𝑦 = − (𝑥 + 3)2 + 4
2
Vertex
y-int
Up/down?
Your turn:
𝑦 = 2(𝑥 − 1)2 + 3
Vertex
y-int
Up/down?
In intercept form:
𝑦 = −(𝑥 + 2)(𝑥 − 4)
x-int
y-int
Up/down?
Vertex
Putting equations in standard form: just simplify!!
a.) 𝑦 = −(𝑥 + 4)(𝑥 − 9)
b.) 3(𝑥 − 1)2 + 8