Quadratics Day 2!
VERTEX FORM
Unit 6 Quadratic Functions
Math II
VERTEX FORM!
y = a(x –
2
h)
+k
-Where a is the same a from Standard Form
-The Vertex of the quadratic is at (h, k)
-We can easily graph a quadratic when it is in vertex form
Converting from Vertex to Standard Form
Example:
y = -2(x – 4)2 + 5
Vertex Form: Square the binomial
Distribute the coefficient
of the trinomial….
= -2(x2 – 8x + 16) + 5
Combine “like” terms
= -2x2 + 16x – 32 + 5
= -2x2 + 16x – 27
Standard Form!
Example: Convert each quadratic to Standard Form.
1. y = 5(x + 2)2 – 9
1. y = -3(x – 4)2 + 7
1. (x – 2)2 + 6
Review Example: Find the Axis of Symmetry of Vertex.
1. y = -2x2 + 4x – 9
1. y = x2 – 10
a = ____, b = ____, c = ____
a = ____, b = ____, c = ____
1. y = x2 + 4x – 1
1. y = -2x2 + 8x – 8
a = ____, b = ____, c = ____
a = ____, b = ____, c = ____
Converting Standard Form to Vertex Form
• Step 1: Determine the a value from standard form
• Step 2: Find the vertex.
– Use x = -b/2a to find the x coordinate
– Substitute x in for the original equation to find y
• Step 3: Substitute vertex and a to vertex form.
Example: Convert the quadratic to Vertex Form.
y=
a=8

2
8x
– 16x + 27
b = -16, c = 27
(16) 16

1
2(8)
16
y  8(1) 2 16(1)  27
(y-coordinate)
y  19
Vertex: (x-coordinate) x 
Vertex: (1, 19)
Vertex Form: y= 8(x – 1)2 + 19
Example: Convert the quadratic to Vertex Form.
y=
2
5x
– 40x + 67
Your turn!: Convert the quadratic to Vertex Form.
1. y = x2 – 9
1. y = 7x2 + 28x + 19
1. y = -2x2 – 24x – 75
Writing the equation of a Quadratic given the
vertex and a point..
Example: Find the equation of the quadratic with vertex
(0, 0) and passes through the point (-2, 8)
y = a(x – 0)2 + 0
Substitute vertex in for h and k
8 = a(-2 – 0)2 + 0
Substitute x and y values in
8 = a(-2)2
8 = 4a
2=a
Simplify and solve for a
Vertex Form: y = 2(x – 0)2 + 0 OR y = 2x2
Example: Find each quadratic function with the given vertex that
passes through the given point. Write in Standard Form.
1. Vertex (2, 0) passing through (1, 3)
1. Vertex (-3, 0) passing through (-5, -4)
1. Vertex (2, 5) passing through (3, 7)
1. Vertex (-3, 4) passing through (0, 0)