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.

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.....