Vertex form:
f(x) = a(x-h)2 + k
This time, it doesn't equal zero, but f(x). If f(x) = x2 + 30x, we need to complete the square
to have it in vertex form, but there's not a zero on the other side to add to, so how do we
keep the equation balanced?
1
Rewrite g(x) = x2 - 10x + 11 in vertex form and identify the vertex.
Same thing for h(x) = 3x2 - 12x - 4
2
Solve x2 = 25 (you can factor, or do it another way)
One way to solve an equation is by getting the squared part by itself.
Reminder: To solve by factoring, you need to get one side to equal 0. This is NOT solving by
factoring. If you cannot factor the original quadratic, solve by completing the square. And
follow the steps on the next page.
3
Solving Quadratic Equations ax2 + bx + c = 0 by Completing the Square:
Example: Solve x2 = 12x - 20
1. Collect variable terms on one side of the equation and constants on the
other.
2. If needed, divide both sides by a to make the coefficient of the x2
term 1.
3. Complete the square
4. Factor the variable expression to make a perfect square
5. Take the square root of both sides of the equation.
6. Solve for x.
4
Solve 18x + 3x2 = 45 by completing the square.
5
Whiteboards
Solve 4x2 + 11 = 59
x2 + 12x + 36 = 28
6
Rewrite f(x) = 3x2 -18x + 7 in vertex form and identify its vertex.
f(x) = 3(x-3)2-20
(3, -20)
7