Converting Quadratic Equations Between Standard And Vertex Form Worksheet
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1
2Converting Quadratic Equations between Standard and Vertex Form
2
2
Standard Form: y = ax
+ bx + c
Vertex Form: y = a(x – h)
+ k
Convert from Standard Form to Vertex Form:
2
2
y = ax
+ bx = c
y = a(x – h)
+ k
know a, b, c
want a, h, k
a
=
a
=
h
Solve for y
=
k
Substitute the values and rewrite.
Example 1:
2
y = 8x
– 16x + 27
We know a, b, c and want a, h, k
2
a = 8
a is the coefficient of the x
term
use the formula to find the value of h
substitute the value found for h into the
2
k = y = 8(1)
– 16(1) + 27 = 8 – 16 + 27 = 19
original equation and solve for k
2
y = 8(x – 1)
+ 19
Example 2:
2
y = 5x
– 40x + 67
We know a, b, c and want a, h, k
2
a = 5
a is the coefficient of the x
term
use the formula to find the value of h
2
k = y = 5(4)
– 40(4) + 67 = 80 – 160 + 67 = –13
substitute the value found for h into the
original equation and solve for k
2
y = 5(x – 4)
– 13
Practice: Convert the following quadratics from standard to vertex form.
2
2
2
1. y = 5x
– 10x + 37
2. y = 7x
+ 28x + 19
3. y = -2x
– 24x – 75
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