A hero is no braver than an ordinary man, but he
is braver five minutes longer.
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
Application
Ex3) A long strip of colored paper is attached as a party decoration at
exactly opposite corners of the back wall of a rectangular party room.
The strip approximates a parabola with equation y = 0.008(x – 25)2 + 10.
The bottom left corner of the back wall is the origin and x and y are
measured in feet. How far apart are the side walls? How high are they?
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 = –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
A hero is no braver than an ordinary man, but he
is braver five minutes longer.