Algebra 1 Common Core Student Edition, Grade 8-9

What feature of

the graph shows

the solutions of the

equation?

Thex-intercepts show

the solutions o f the

equation.

How do you know
you can solve using
square roots?
The e q u a tion has an
x 2-te rm and a co n sta n t
term, but no x-term.
So, y o u can w r i t e th e
e q u a tio n in th e fo rm
x 2 = k and then find the
square roots o f each side.

So l v i n g b y Gr a p h i n g

What are the solutions of each equation? Use a graph of the related function.

Ox 2 - 1 = 0

Graph y = x2 — 1.

There are two

solutions, ± 1.

Qx 2 = o

Graph y = x2.

ty^4

\ 1 J

\

V

X

0

(^1) I-
There is one
solution, 0.
Qx2 + i = o
Graph y = x2 + 1.
There is no real-number
solution.
Go t I t? 1. What are the solutions of each equation? Use a graph of the related
function.
a. x 2 - 16 = 0 b. 3 x 2 + 6 = 0 c. x 2 - 25 = - 2 5
You can solve equations of the form x2 = k by finding the square roots of each side.
For example, the solutions of x2 = 81 are ± VfU, or ± 9.
Pr o b l em 2 So l v i n g U si n g Sq u a r e Ro o t s
What are the solutions of 3x 2 - 75 = 0?
Thirm
Write the original
equation.
Write
3x2 - 75 = 0
Isolate x 2 on one side of
the equation.
Find th e square roots o f
each side and simplify.
3x2 = 75
x2 = 25
x = ± V 2 5
x = ± 5
( J Got It? 2. What are the solutions of each equation?
a. m 2 - 3 6 = 0 b. 3 x 2 + 15 = 0 c. 4d2 + 16 = 16
5 6 2 Chapter 9 Quadratic Functions and Equations