Objectives:
• Be able to graph a quadratic function in
vertex form
• Be able to write a quadratic function
in vertex form (2 ways)
Vertex Form of a Quadratic
Parent Function:
Vertex Form of a Quadratic Equation:
y  x2
f ( x )  a ( x  h) 2  k
5
4
3
2
1
-5 -4 -3 -2 -1
1
-1
-2
-3
-4
-5
2
3
4
5
Reflection over x-axis
if a is negative,
vertical stretch (a > 1)
or shrink (a < 1)
Vertical
Translation
Horizontal
translation
(opposite of what
you see!)
*The vertex of the parabola is (h, k) and the axis of symmetry is x = h.
Graphing Equations in Vertex Form
1
2
Ex 1) y   ( x  2)  3
2
a. Vertex (horiz. and vert. translation)
10
8
b. Axis of symmetry
6
c. Table
4
2
-10 -8 -6 -4 -2
2
4
6
8 10
x
•
Point
•
Vertex
•
Corresp.
-2
-4
-6
-8
-10
d. Ask:
•
Correct reflection?
•
Correct stretch or shrink?
y
Try this one…
Ex 2) f ( x)  2( x  1)  4
2
a. Vertex (horiz. and vert. translation)
10
8
b. Axis of symmetry
6
c. Table
4
2
-10 -8 -6 -4 -2
2
4
6
8 10
x
•
Point
•
Vertex
•
Corresp.
-2
-4
-6
-8
-10
d. Ask:
•
Correct reflection?
•
Correct stretch or shrink?
y
Vertex Form from Graph
Ex 4) Write the equation for the following parabola in vertex form:
y = a(x – h)2 + k
Vertex Form from Graph
Ex 4) Write the equation for the following parabola in vertex form:
y = a(x – h)2 + k
Vertex Form from Standard Form
Ex5) Write y = 2x2 + 10x + 7 in vertex form.
a. Find the x-coordinate of the vertex (h):
b
2a
b. Find the y-coordinate of the vertex (k):
c. Substitute a, h, and k into vertex form:
y  a ( x  h)  k
2
Vertex Form from Standard Form
Ex5) Write y = –7x2 – 70x – 169 in vertex form.
a. Find the x-coordinate of the vertex (h):
b
2a
b. Find the y-coordinate of the vertex (k):
c. Substitute a, h, and k into vertex form:
y  a ( x  h)  k
2