Zero Product Property and Factoring

Zero Product Property and Factoring

Unit 9 Quadratics

Agenda (3/7/22):

• ​Interactive Notes on Zero Product Property and Factoring

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• Homework: 2 Khan Academy assignments on solving quadratics by factoring. Work not required.

Objectives (SWBAT):

• Solve quadratic equations using the zero product property

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• Factor quadratic equations using one of the methods from unit 8

What is a Quadratic Equation?

• A quadratic equation is an equation in which the highest power of the variable is a square. 

• Highest Power = exponent

• Square = degree of 2

Multiple Select

Which of the equations below are quadratic?

Select all that apply.

• $$0=3x^2+4x+3$$  

• $$7=\frac{1}{2}x+5$$  

• $$0=-10x^{2\ }$$  

• $$5=x^2+x^3$$  

Multiple Choice

Read the sentence and select what you think goes into the blank

Solutions to any quadratic equation are the _________ on a graph.

• x-intercepts

• y-intercept

• vertex

• axis of symmetry

Poll

Read the sentence and select what you think goes into each blank

A quadratic function can have ____, ____ or ____ solutions.

• 0

• 1

• 2

• 3

• infinite

Multiple Select

Read the sentence and select what you think goes into the blanks

The solutions to a quadratic equation are also called the _____, or ______.

• zeros

• roots

• maximum

• minimum

Open Ended

Look at the algebraic definition in the concept map.

Do you think a and b can both be 0 at the same time? Explain.

Open Ended

Look at the application in the concept map.

Why must the expression be factored before using the Zero Product Property?

Open Ended

Look at the example in the concept map.

Type out what should be in each box.

Fill in the Blanks

In the previous slide,

$3x\left(x-7\right)=0$  can be split up using the zero product property into  $3x=0$  and  $x-7=0$ . If we solve for each equation, what are our two values for  $x$  ? 

Type answer like x = number 1, number 2

Open Ended

Look at the example in the concept map.

Type out what should be in each box.

Fill in the Blanks

In the previous slide,

$\left(2x-3\right)\left(x+9\right)=0$  can be split up using the zero product property into  $2x-3=0$  and  $x+9=0$ . If we solve for each equation, what are our two values for  $x$  ? 

Type answer like x = number 1, number 2

Multiple Choice

Use the zero product property to find the solutions for the quadratic equation shown below.

$$\left(5x-1\right)\left(x+2\right)=0$$  

• $$x=-2,\ \frac{1}{5}$$   

• $$x=2,\ \frac{1}{5}$$  

• $$x=2,\ 5$$  

• $$x=-2,\ 5$$  

Multiple Choice

Use the zero product property to find the solutions for the quadratic equation shown below.

$$\left(x+4\right)\left(2-x\right)=0$$  

• $$x=-4,\ 2$$  

• $$x=-4,\ -2$$  

• $$x=4,\ 2$$  

• $$x=4,\ -2$$  

Factoring to Solve Quadratic Equations

• Zero Product Property can only be used if a Quadratic Equation is already factored.

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• In general, you will need to factor a Quadratic Equation using one of the methods from the last unit.

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• Once you factor, use the zero product property to find the solutions to the Quadratic Equation.

Multiple Choice

What is the factored form of

$$x^2+2x-24=0$$  ? 

• $$\left(x-6\right)\left(x+4\right)=0$$  

• $$\left(x-3\right)\left(x+8\right)=0$$  

• $$\left(x+6\right)\left(x-4\right)=0$$  

• $$\left(x+2\right)\left(x-12\right)=0$$  

Multiple Choice

The factored form of

$$x^2+2x-24=0$$  is  $$\left(x-4\right)\left(x+6\right)=0$$  . What are the solutions? Use the Zero Product Property.

• $$x=-4,\ -6$$  

• $$x=4,\ 6$$  

• $$x=-4,\ 6$$  

• $$x=4,\ -6$$  

Multiple Choice

What is the factored form of  $$2x^2-3x-2=0$$  ?

• $$\left(2x-2\right)\left(x+1\right)=0$$  

• $$\left(2x+1\right)\left(x-2\right)=0$$  

• $$\left(2x+2\right)\left(x-1\right)=0$$  

• $$\left(2x-1\right)\left(x+2\right)=0$$  

Multiple Choice

The factored form of  $$2x^2-3x-2=0$$  is  $$\left(2x+1\right)\left(x-2\right)=0$$  . What are the solutions?

• $$x=-3,\ -2$$  

• $$x=2,\ -3$$  

• $$x=-2,\ \frac{1}{2}$$  

• $$x=-\frac{1}{2},\ 2$$  

Open Ended

What questions do you have after completing this Quizizz lesson?