zero product property...x2 + 4x = 21. solving quadratic equations solve the equation by factoring....

Zero Product Property

Algebra 1

How do I get ready for class? 1) On Desk: binder, pens/pencils2) You are tardy if you are not in your seat when the bell rings

Homework: Zero Product Property

Upcoming……Quiz Today!

Warm Up: Factor the following quadratic expressions.

1) 𝑥2 − 100 2) 𝑝2 − 36 3) 𝑥2 − 12𝑥 + 36

Homework Review

Now Grading:

• Special Products

Any Questions?

Standards

MGSE9–12.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

MGSE9–12.A.SSE.3a Factor any quadratic expression to reveal the zeros of the function defined by the expression.

What do you already know about

these standards?

Quadratic Graphs

Finding Zeros on Quadratic Graphs

Find the zeros of the following graphs and then factor the quadratic expression.

Finding Zeros on Quadratic Graphs

What do you notice about the zeros and the factored form of the equation?

What is the value of y when the parabola crosses the x-axis for each graph?

Zero Product Property (ZPP)

The zero product property is used to solve an equation when one side is zero and the other side is a product of binomial factors.

If 𝒂 ∙ 𝒃 = 𝟎, the _______ or _________.

What it means: If we have two algebraic expressions equal to zero, then one of the expressions is equal to zero.

Solving by Factoring and using the Zero Product Property

1. Get all terms together on one side of the equation.

2. Set one side equal to zero.

3. Factor completely, if necessary.

4. Set each factor equal to zero.

5. Solve and list solutions as x = ________.


Solve each equation by using the Zero Product Property.

1. (x – 2)(x + 4) = 0 2. x (x + 4) = 0



3. 𝑦 = 𝑥2 − 6𝑥 + 9



4. 𝑥2 + 4𝑥 = 32

Quiz

• Write in pencil ONLY

• Show ALL work to receive full credit

• When you turn in your quiz, bring your notebook

• Your notebook should have

– Completed Table of Contents

– All pages glued in and filled out

– Current numbered pages



1) x (x + 2) = 0 2) 2x ( x – 5) = 0

3) (n – 5) (n + 3) = 0 4) (x – 3) (x + 1) = 0

Solving Quadratics Using the Zero Product Property


Solve by factoring completely and using the Zero Product Property.


Homework #3 & 4



If the product of two quantities equals zero, at least one of the quantities equals zero.

Example: 3(0) = 0 0(4) = 0

Zero of a Function

Zero of a function

• x-value that makes the function equal 0

• x-intercept of the function (y = 0)

• Also known as a root of the quadratic

NOTE: Solving a quadratic equation means finding its zeros!

Solving by Factoring

Solving a Quadratic Equation

• Replace f(x) with 0.

• Solve ax2 + bx + c = 0

Remember: Solving a quadratic equation means finding its zeros!

Solving Quadratic Equations

Find the zeros of the following function.

f(x) = (x – 7)(x + 2)


Use the Zero Product Property find the zeros of the function. Check your answer.

f(x)=(x – 2)(x)


Use the Zero Product Property to solve the equation. Check your answer.

f(x) = (x + 4)(x – 3)

Solving Quadratic Equations using Factoring

Sometimes you may need to factor before using the Zero Product Property to solve an equation.


Solve the equation by factoring. Check your answer.

f(x) = x2 +14x + 49



x2 + 4x = 21



x2 – 12x + 36 = 0

Quiz

List the first 15 perfect squares.

Homework/Classwork

Homework: Page 575

• Return Tests

• Test Corrections

– Parent signature

– Need to come to at least one help session

– Corrections need to be done by next Wednesday

Thursday April 1, 2015

How do I get ready for class? 1) On Desk: binder, pens/pencils, textbook

Homework: Page 441 and Page 451 (#1-10)

Upcoming……Quiz today

Warm Up: No Warm Up

Get ready for your quiz (You have 15 minutes after the bell)

Carefully tear pages 441 and 451 from your book.



f(x) = x2 +10x + 25



x2 – 6x + 9 = f(x)



x2 + 4x = 5



30x = –9x2 – 25



3x2 – 4x + 1 = 0


The height in feet of a diver above the water can be modeled by h(t) = –16t2 + 8t + 8, where t is time in seconds after the diver jumps off a platform. Find the time it takes for the diver to reach the water.


The equation for the height above the water for another diver can be modeled by h = –16t2 + 8t + 24. Find the time it takes this diver to reach the water.

Homework/Classwork

Homework: Page 557

Show work on a separate sheet.





Friday February 5, 2016

How do I get ready for class? 1) On Desk: binder, pens/pencils

Homework: Page 577 (even) and Page 585 (even)

Upcoming……Quiz today

Warm Up: No Warm Up

Get ready to grade your homework.

Monday February 8, 2016

How do I get ready for class? 1) On Desk: binder, pens/pencils

Homework: Page 585 (odd)

Upcoming……

Warm Up: Solve the following using square roots.

1) 𝑥2 − 121 = 0 2) (𝑥 − 2)2= 49

3) 2𝑥2 − 36 = 0 4) 𝑥2 + 4 = 25

Homework/Classwork

Page 577 (odd) and Page 585 (odd)





zero product property...x2 + 4x = 21. solving quadratic equations solve the equation by factoring....

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