Unit 7 Lesson 5

Unit 7 Lesson 5:

How Many Solutions

5.1: Math Talk - Decide whether each statement is true or false.

Poll

3 is the only solution to

 $x^2-9=0$  

• True

• False

Poll

A solution to

 $x^2+25=0$  
is -5

• True

• False

Poll

 $x\left(x-7\right)=0$  has two solutions.

• True

• False

Poll

 $\left(x-5\right)\left(x+7\right)=12$  

5 and -7 are the solutions to

• True

• False

Act. 5.2: Solving by Graphing

Han is solving three equations by graphing:

(x - 5)(x - 3) = 0

(x - 5)(x - 3) = -1

(x - 5)(x - 3) = -4

Act. 5.2 #1

To solve the first equation $\left(x-5\right)\left(x-3\right)=0$  

he graphed 
 $y=\left(x-5\right)\left(x-3\right)$  
and then looked for the x-intercepts of the graph.

Open Ended

Explain why the x-intercepts can be used to solve

 $\left(x-5\right)\left(x-3\right)=0$  

What are the solutions?

Act. 5.2 #2

To solve the second equation, Han wrote it as

 $\left(x-5\right)\left(x-3\right)+1=0$  

He then graphed 
 $y=\left(x-5\right)\left(x-3\right)+1$  
Use graphing technology to graph this, and use graph to solve equation.

Act. 5.3

• #3. Solve the third equation using Han's strategy.

• Thinking about the strategy we used:

• a) Why might it be helpful to rearrange each equation to equal 0 on one side and then graph the expression on the non-zero side?

• b)How many solutions does each of the three equations have?

Act. 5.3 Finding All the Solutions

• 1.  $x^2=121$  

• 2.  $x^2-31\ =\ 5$  

• 3..  $\left(x-4\right)\left(x-4\right)=0$  

• 4.  $\left(x+3\right)\left(x-1\right)=5$  

• 5.  $\left(x+1\right)^2=-4$  

• 6.  $\left(x-4\right)\left(x-1\right)=990$