Graphing Quadratic Equations

Graphing Quadratic Equations

We will graph quadratic equations by creating a table.

Essential Question

How do the key attributes aid in graphing quadratic equations?

Bring it back....

Lets review quadratic equations so far...

Multiple Choice

What is a axis of symmetry?

• all real numbers

• y=5

• the line that divides the graph in equal halves

• y=mx+b

Multiple Choice

What is the domain of the graph shown above.

• x=19

• all real numbers

• y=3

• Maximum

Multiple Choice

What do we call the highest or lowest point of a quadratic?

• parabola

• vertex

• graph

• point

Multiple Choice

What is the vertex?

• (2, 4)

• (3, -1)

• (0, 8)

• (4, 2)

Multiple Choice

What is the vertex? (*Remember a(x-h)²+k, where (h,k) is the vertex)

f(x) = 2(x - 5)² + 12

• (-5, -12)

• (5,-12)

• (5, 12)

• (-5, 12)

Multiple Choice

What is the vertex?

y = -2x² + 4x + 3

(Use -b/2a to help find the vertex)

• (0, 3)

• (-1, 5)

• (1, 5)

• (1, -5)

Where yo notes at?

Make sure to take some notes...

Graphing Quadratic Equations

Step 1: Find the axis of symmetry by x = -b/2a

Step 2: Find the vertex.

Substitute x-value into the equation to obtain the y-value of the vertex.

Step 3: Create a table with coordinate points 2 points on both sides of the line of symmetry.

  $f\left(x\right)=2x^2-4x-1$ Step 1: Line of Symmetry

Remember  $f\left(x\right)=ax^2+bx+c$ .
So using  $x=\frac{-b}{2a}$  , we see that 
a=2, and b=-4 -->    $x=\frac{-\left(-4\right)}{2\left(2\right)}=1$  

 $f\left(x\right)=2x^2-4x-1$  
Step 2: Find the vertex

Since  $x=\frac{-b}{2a}=1$  , the substitute back into f(x).  So  $f\left(1\right)=2\left(1\right)^2-4\left(1\right)-1=3$  
The vertex (h,k) is (1,-3)

 $f\left(x\right)=2x^2-4x-1$ Step 3:  Create a table

Begin with the vertex as the center point on the table.  
Next find the two points on both sides of the line of symmetry.  (Think on 2 values on the left and the right of symmetry)

Lets groove

Take 2 minutes to discuss with a partner on the next slide and put your answers in the chat and in the lesson.

Fill in the Blanks

What do you notice about to values of f(x)? *Remember y=f(x).

Use this stem: The values of f(x)__________on both sides of the___________

Let's Practice

We will find the line of symmetry, the vertex and the matching graphs of quadratic equations.

Multiple Choice

What is the axis of symmetry for the equation y=-x²+4x+3

• x=2

• y=2

• x=-2

• y=-2

Multiple Choice

What is the vertex of the quadratic equation y=-x²+4x+3?

• (0,3)

• (2,7)

• (-2,7)

• (3,0)

Multiple Choice

What is the line of symmetry?

f(x) = -x² - 4x + 12.

• x = -1

• x = 12

• x = -4

• x = -2

Multiple Choice

What is the vertex?

f(x) = -x² - 4x + 12.

• (-2, 16)

• (2, 0)

• (2, 4)

• (-2, 4)

Multiple Choice

What is the value of Y if x+{-2,-1,0,1,2} for  $y=-x^2-2x+5$  

• x={-3,2,5,6,5}

• x={-2,-1,0,1,2}

• x={5,6,5,2,-3}

• x={5,5,5,5}

Multiple Choice

What is the value of Y if x ={-2,-1,0,1 2} for  $y=x^2+3x$  

• y={10,4,0,-2,-2}

• y={-2,-2,0,4,10}

• y={-2,0,0,4,10}

• y={-2,-2,-2,-2}

Multiple Choice

What is the graph of y = -3x² + 12x - 16

Multiple Choice

Which table represents the parent function

 $y=x^2$  

Multiple Choice

Graph the equation

• A

• B

• C

• D

Multiple Choice

Graph the equation

• A

• B

• C

• D

Multiple Choice

Graph the equation

• A

• B

• C

• D

Open Ended

How do the key attributes aid in graphing quadratic equations? (Ex: vertex, line of symmetry, y-intercept, roots) Choose at least 1 attribute.

The _______ helps with graphing because.....