Complete the Square Worksheet
First let’s do one that has a shape factor of 1
5x4x)x(f
2
Put the first two terms inside parentheses and leave a space:
5)x4x()x(f
2
take “b” the coefficient of the x term, divide it by 2 and square the result. Put this in the
parentheses:
5)4x4x()x(f
2
Now, you’ve added 4 to right hand side of the equation…so to rebalance the equation,
add 4 to the right hand side.
45)4x4x()x(f
2
Now, the terms in the parentheses are a perfect square:
9)2x()x(f
2
The parabola was shifted left 2 and pulled down 9.
The vertex is a ( 2, 9) Recall:
k)hx()x(f
2
You have to put in “” to replace the “+” in the parentheses and a homemade + sign in
between the squared term and the number 9 to get the correct (h, k).
What are the x and y intercepts:
The y intercept is the point with x = 0…f(0)= (
59)20
2
. ( 0, 5)
The x intercepts have a y value of 0….
x1or5
2x3
)2x(9
9)2x(0
2
2
(5, 0) and ( 1, 0)
Now you do one:
2x6x)x(f
2
