Completing the Square - Jan. 5

Completing the Square - Jan. 5

"I can solve equations and rewrite functions by completing the square."

Time for Review

Quadratic Equations- is a non-linear equation. It must have a square.

Multiple Choice

REVIEW: The graph of a quadratic function is called

• a line

• a hyperbola

• a parabola

• a cubic

Multiple Choice

REVIEW: Standard form of a quadratic equation

• y=x²

• y=ax²+bx+c

• y=mx+b

• y=x

Multiple Choice

REVIEW: 3x² - 4 is a quadratic

• true

• false

Multiple Choice

REVIEW: Which of the following is NOT a quadratic function

• f(x) = -3x²

• f(x) = -5x - x²

• y = 3x³ - 4x + 5

• A = pi.r²

Multiple Choice

REVIEW: What are the dots called?

• axis of symmetry

• vertex

• parabola

• roots or x-intercepts

Open Ended

This lesson has 3 key concepts.

GOAL: I can solve show mastery in solving equations and rewriting functions by completing the square.

Type or write the goal statement above.

Open Ended

The transcendentals (Latin: transcendentalia) are the three properties of being: truth, beauty, and goodness. In regards to today's topic, how do you feel this relates to truth, beauty or goodness in your life or as a contribution to the lives around you? Another words: Why is learning completing the square important in regards to the pursuit of truth, beauty and/or goodness?

Open Ended

KEY CONCEPT: SOLVING BY FINDING SQUARE ROOTS.

What is the solution of the equation

 $4x^2+10x=46$  

Open Ended

Solve the equation by using the Square Root Property. Round to the nearest hundredth if necessary. $100\ x^2-60\ x+9=121$   

Open Ended

Solve the equation by using the Square Root Property. Round to the nearest hundredth if necessary.

 $x^2-18x+81=49$  

Multiple Choice

If I isolate the variable and THEN take the square root, I ______________get the right answer.

• WILL

• WILL NOT

Multiple Choice

If I take the square root BEFORE isolating the variable, I ___________________ get the right answer.

• WILL

• WILL NOT

Multiple Choice

Why is there a

 $\pm$  for the answer solutions?

• When you take the square root, there is a positive and negative solution.  

• In real world problems, a negative solution may not make sense.  

• All of the above

Multiple Choice

How is solving by finding square roots similar to solving for a linear equation?

• You isolate the variable

• You always have to graph to find the solution

Multiple Choice

Sometimes we must rewrite the equation in order to solve. This is why it is important to know how to make a perfect square trinomial.

• True

• False

Open Ended

KEY CONCEPT: MAKING A PERFECT SQUARE TRINOMIAL.
What is the solution of 

 $x^2+4x+4=25$  

Open Ended

Find the value of c that makes the trinomial a perfect square. Then write the trinomial as a perfect square.

 $x^2-3\ x\ +c$  

Open Ended

Find the value of c that makes the trinomial a perfect square. Then write the trinomial as a perfect square.

 $x^2+60\ x+c$  

Multiple Choice

What happens if the constant on the right side is not a perfect square?

• The answers are irrational (An irrational number is a number that cannot be expressed as a fraction for any integers and irrational numbers have decimal expansions that neither terminate nor become periodic.).

• It must always be a perfect square. There are times when it is not possible to complete the square and this is an example.

Open Ended

Find the value of c that makes the trinomial a perfect square. Then write the trinomial as a perfect square.

 $x^2+60\ x+c$