Section 9.1C: Graphing Quadratic Functions in Vertex Form
Guided Notes
Honors Algebra I
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Date: _________________________________
Learning Targets

I can graph a quadratic in vertex form using the vertex and a table.
Quadratic Function in Vertex Form
𝑓(𝑥 ) = 𝑎(𝑥 − ℎ)2 + 𝑘
Direction/Steepness
x Value of Vertex
> If a is positive, the graph opens up.
*Note: this value appears
> If a is negative, the graph opens down.
to be flipped!
> As a approaches zero, the graph widens.
Example
Graph 𝑓(𝑥) = (𝑥 − 4)2 − 3
Vertex: (4, −3)
*Use a table to complete graph.
*There is a shortcut, too!
𝑥
2
3
4
5
6
y Value of Vertex
𝑦
1
−2
−3
−2
1
Work Shown
𝑓(2) = (2 − 4)2 − 3 = 1
𝑓(3) = (3 − 4)2 − 3 = −2
Given by Vertex Form.
Reflected from (2,1)
Reflected from (3, −2)
Examples (finding the vertex)
Find the vertex of each parabola without graphing.
1
a)
𝑦 = 2(𝑥 − 3)2 + 5
b)
𝑦 = 3 (𝑥 − 1)2 − 3
d)
𝑓(𝑥) = 𝑥 2 + 8
e)
𝑦 = 2 (𝑥 + 3)2
1
c)
𝑓(𝑥) = (𝑥 + 5)2 + 9
f)
𝑦 = − 3 (𝑥 − 7)2 − 1
2
Examples (graphing in vertex form)
First, identify the vertex. Then make a table around this value to complete the parabola.
a)
𝑦 = (𝑥 − 2)2 + 5
x
d)
b)
𝑦 = (𝑥 + 6)2 − 8
x
y
𝑦 = −(𝑥 − 1)2 + 5
c)
x
y
x
y
e)
1
𝑓(𝑥) = 2 (𝑥 − 1)2 + 6
y
𝑦 = (𝑥 + 5)2
x
y