Intro to Factored Form Quadratics

Standard and Factored Quadratics

Overview and Review

Previously...

We worked on the parts of Standard Form quadratics, factoring with the "AC method", and using the Zero Product Property to solve Factored Form Quadratics.

We'll review these ideas in the next slides

Fill in the Blanks

$7x^{2\ }-13x+4$  

Given the quadratic expression above, what is the value of  `b` ? 

Fill in the Blanks

$5x-3+x^2$  

Given the quadratic expression above, what is the value of  `b` ? 

Fill in the Blanks

$x^2-4x+3$  

Given the quadratic expression above, what is the value of  `a` ? 

Fill in the Blanks

$2x^2-x-4$  

Given the quadratic expression above, what is the value of  `b` ? 

Fill in the Blanks

$x^2+2x$  

Given the quadratic expression above, what is the value of  `c` ? 

Standard Form

Always written in order of highest degree to lowest degree.

Then we can clearly identify a, b, c in order to use the "AC Method" to convert quadratics into Factored Form.

Multiple Choice

$$x^2-6x-16$$  
Write the quadratic above in Factored Form.

• $$\left(x-4\right)\left(x+4\right)$$  

• $$\left(x-2\right)\left(x+8\right)$$  

• $$\left(x-8\right)\left(x+2\right)$$  

Multiple Choice

$$x^2-2x-15$$  
Write the quadratic above in Factored Form.

• $$\left(x+3\right)\left(x-5\right)$$  

• $$\left(x-3\right)\left(x+5\right)$$  

• $$\left(x-30\right)\left(x+17\right)$$  

• $$\left(x+30\right)\left(x-17\right)$$  

Multiple Choice

$$x^2-6x+8$$  
Write the quadratic above in Factored Form.

• $$\left(x+2\right)\left(x-4\right)$$  

• $$\left(x-2\right)\left(x-4\right)$$  

• $$\left(x+2\right)\left(x+4\right)$$  

• $$\left(x-2\right)\left(x+4\right)$$  

Zero Product Property

If the result of a product is zero, one or more of the factors must be equal to zero.

We can use this property to find the "zeros" or solutions to a quadratic.

Multiple Select

$$\left(x+3\right)\left(x-2\right)=0$$  

Select the 2 solutions to this quadratic.

• $$x=3$$  

• $$x=-3$$  

• $$x=2$$  

• $$x=-2$$

Multiple Select

$$\left(3x+8\right)\left(x+1\right)=0$$  

Select the 2 solutions to this quadratic.

• $$x=\frac{8}{3}$$  

• $$x=-\frac{8}{3}$$  

• $$x=1$$  

• $$x=-1$$

Multiple Select

$$\left(2x-3\right)\left(3x-1\right)=0$$  

Select the 2 solutions to this quadratic.

• $$x=\frac{3}{2}$$  

• $$x=-\frac{3}{2}$$  

• $$x=\frac{1}{3}$$  

• $$x=-\frac{1}{3}$$

That's it for Now!

• Standard Form Structure

• "AC Method" for Factoring

• Zero Product Property for Solving

• >>> That paper triangle only has one side..... >>>