Name______________________________
Date: _________________ Block:_______
Ms. Gallagher
We can solve quadratic equations that are written in vertex form by taking the square
root of both sides.
EXAMPLE ONE Solve the following solutions
2(x – 3)2 + 10 = 28
(x + 5)2 – 12 = –31
–3(x – 1)2 + 4 = 1
EXAMPLE TWO Write the equation in vertex form and solve by finding the square root
2x2 – 8x = 5
Quadratic equations can also be solved when they are written in intercept form by
using the zero product property.
Zero Product Property
If A and B are expressions and AB = 0
The A = 0 or B = 0
This is why it is easy to solve quadratics in intercept form, or factored form.
EXAMPLE THREE Factor the following quadratic expression and solve.
x2 + 4x = 12
2r – 63 = –r2
n2 = 9n – 20
EXAMPLE FOUR Factor the following quadratic expression and solve.
5x2 – 17x = –6
3g2 – 7 = –20g
4u2 + 12u = –5
4x2 + 2 = 9x
EXAMPLE FIVE You have made a rectangular quilt that is 5 feet by 4 feet. You want to
use the remaining 10 square feet of fabric to add a decorative border of uniform width
to the quilt. What should the width of the quilt’s border be?
EXAMPLE SIX A town has a nature preserve with a rectangular field that
measures 600 meters by 400 meters. The town wants to double the area
of the field by adding land as shown. Find the new dimensions of the field.
Homework 4.3 # 33 – 38, 53, 54, 55,
4.4 # 6 – 11, 15, 16, 36 – 40, 62, 63