Algebra 1 Common Core Student Edition, Grade 8-9

Got It? 3. Find the vertex of each parabola using the method of completing the square.

a. y = x2 + 4x + 10 b. y = x2 + 12x + 34

The method of completing the square works when a = 1 in ax2 + bx + c = 0. To solve

an equation when a # 1, divide each side by a before completing the square.

Pr o b l em 4

Th i n k
Why do you need to
find 1 ( f )?

To make a perfect-square
trin o m ia l on th e le ft side
of x2 + |x = 32, find
^j.Then square the
result and add to each
side o f the equation.

Co m p l et i n g t h e Sq u a r e W h e n a ^ 1

Gardening You are planning a flower

garden consisting of three square plots

surrounded by a 1-ft border. The total area

of the garden and the border is 100 ft2.

What is the side length x of each square plot?

• Area of garden and border


• Expressions fo r th e d im e n sio n s o f th e garden
  and border.

^5 Red tulips Yellow tulips

The side length x o f each

square plot

Write and solve an equation that

relates the dimensions and area of

the garden and border.

Step 1 Write an equation that you can use to solve the problem.

(3x + 2)(x + 2) = 100 Length X Width = Area

3x2 + 8x + 4 = 100 Find the pro d u ct (3x + 2)(x + 2).

3x2 + 8x = 96

XZ + gX = 32

Step 2 Complete the square.

x2 + |x + y = 32 + y

I , 4 I 2 _ 3 0 4

[X 3 J 9

S te p 3 Solve the equation.

Subtract 4 from each side.

Divide each side by 3.

Add 11 j 2, or y , to each side.

Write left side as a square and right side as a fraction.

x + l = + ./ 3 0 4X -r 3 - V g

X +

X +

±5.81

5.81

4.48

Find square roots o f each side.

Use a c a lc u la to r to a p p r o x im a te \ /

or

or

x + -5.81 Write as two equations.

-7.14 S olve f o r x.

The negative answer does not make sense in this problem. So the side length of each

square plot is about 4.48 ft.

578 Ch ap t er 9 Quadratic Functions and Equations