Perfect Square Equations HONORS

Perfect Square Equations

Multiple Choice

BELLWORK: Simplify: √20

• 2√5

• 4√5

• 5√2

• 2√10

Open Ended

BELLWORK: When solving a quadratic equation, such as x²+9x-36=0, what do the solutions mean in terms of graphing?

Multiple Select

BELLWORK: Google "different names for x-intercepts" and select all terms that are used to refer to x-intercepts on a graph.

• zeros

• solutions

• y-intercepts

• roots

• branches

Open Ended

BELLWORK: Use your resources (the internet or past knowledge) to answer the following question:

What is the difference between a rational and an irrational number? Provide an example of both.

STOP

When solving with square roots, you must consider the positive AND the negative solution.

Example 1: x²=25

Example 2: (x-1)²=4

Example 3:

Solve (x-3)²-4=0

*Perfect Square Form*

Example 3:

Solve (x-3)²-12=0

*Approximate vs. Exact Form*

Fill in the Blanks

Solve  $\left(x+4\right)^2-20=0$  .

Write your answer as x=a,b without spaces and writing

 $\sqrt{a}$  as sqrt(a). For example:  $2\sqrt{5}-4$  =2sqrt(5)-4.

Simplify radicals (square roots)! If there is no solution, write "no real solution".

Fill in the Blanks

Find the zeros of $\left(2x-3\right)^2-49=0$  .

Write your answer as x=a,b without spaces and writing

 $\sqrt{a}$  as sqrt(a). For example:  $2\sqrt{5}-4$  =2sqrt(5)-4.

Simplify radicals (square roots)! If there is no solution, write "no real solution".

Fill in the Blanks

Find the solutions to $\left(7x-5\right)^2+2=0$  .

Write your answer as x=a,b without spaces and writing

 $\sqrt{a}$  as sqrt(a). For example:  $2\sqrt{5}-4$  =2sqrt(5)-4.

Simplify radicals (square roots)! If there is no solution, write "no real solution".

Fill in the Blanks

Find the roots of $\left(5-10x\right)^2=0$  .

Write your answer as x=a,b without spaces and writing

 $\sqrt{a}$  as sqrt(a). For example:  $2\sqrt{5}-4$  =2sqrt(5)-4.

Simplify radicals (square roots)! If there is no solution, write "no real solution".

Fill in the Blanks

Solve  $\left(x+2\right)^2=-10$  .

Write your answer as x=a,b without spaces and writing

 $\sqrt{a}$  as sqrt(a). For example:  $2\sqrt{5}-4$  =2sqrt(5)-4.

Simplify radicals (square roots)! If there is no solution, write "no real solution".

Fill in the Blanks

Solve $\left(x+11\right)^2+5=5$  .

Write your answer as x=a,b without spaces and writing

 $\sqrt{a}$  as sqrt(a). For example:  $2\sqrt{5}-4$  =2sqrt(5)-4.

Simplify radicals (square roots)! If there is no solution, write "no real solution".

Fill in the Blanks

Find the x-intercepts of $y=\left(x-6\right)^2-15$  .

Write your answer as x=a,b without spaces and writing

 $\sqrt{a}$  as sqrt(a). For example:  $2\sqrt{5}-4$  =2sqrt(5)-4.

Simplify radicals (square roots)! If there is no solution, write "no real solution".

Fill in the Blanks

CHALLENGE: Find the x-intercepts of $y=2\left(x+3\right)^2-50$  .

Write your answer as x=a,b without spaces and writing

 $\sqrt{a}$  as sqrt(a). For example:  $2\sqrt{5}-4$  =2sqrt(5)-4.

Simplify radicals (square roots)! If there is no solution, write "no real solution".

Fill in the Blanks

CHALLENGE: Find the roots of $y=-\frac{1}{2}\left(3x-7\right)^2+2$  .

Write your answer as x=a,b without spaces and writing

 $\sqrt{a}$  as sqrt(a). For example:  $2\sqrt{5}-4$  =2sqrt(5)-4.

Simplify radicals (square roots)! If there is no solution, write "no real solution".