1. Graphs of Quadratic Functions Part 1
UPDATE!!!
Graphs of Quadratic Functions Part 1

2. Graph Quadratic Functions:
Standard Form: y = ax2 + bx + c
Shape: Parabola
When in standard form,
If a is positive, the parabola opens up y = ax2+bx+c
If a is negative, the parabola opens down y = -ax2+bx+c

3. Will It Open Up or Down? y = 4x2 + 7x – 4 y = -6.5x2 + 9
*must be in standard form

4. Parts of Parabolas: Axis of Symmetry:
Vertex:
Highest or lowest point of the graph
(the max or min of the function)
Lies on the axis of symmetry
Axis of Symmetry:
Line of symmetry that divides parabola into two parts that are mirror image of each other.
Cuts through the vertex
Axis of Symmetry
Vertex

5. The axis of symmetry is the vertical line passing through
y = ax2+bx+c
Find Vertex and Write the equation of the axis of symmetry for y = 3x2+8x-6
1st: Identify a, b, and c
2nd: Plug into
a=3, b=8, c=-6
Axis of symmetry is vertical line x= -4 3

6. Find the vertex of y = 3x2+8x-6 Continued…
3rd: Plug x value into function to solve for y
y = 3( −4 3 )2 + 8 ( −4 3 ) - 6
The vertex has an x-coordinate of −𝑏 2𝑎
Because it lies on the axis of symmetry
y = 3( 16 9 ) + 8 ( −4 3 ) - 6
y =
y =
Vertex is point (-1 𝟏 𝟑 , -11 𝟏 𝟑 )

7. x=0 is the axis of symmetry
Find the Vertex and Graph:
y = x2
First find the vertex.
y = ax2+bx+c a=1, b=0, and c=0
x=0 is the axis of symmetry
This is also the x value of the vertex, now find the y value. If x = 0, y = (0)2
Vertex = (0,0)

8. Since the vertex is (0,0), pick an + and a - x value
Example: y = x2
Make a table for y = x2
Once you find the vertex, pick at least 2 more points to see how to graph the parabola, plot them and their mirror images to make it symmetrical
Since the vertex is (0,0), pick an + and a - x value
Once you find the vertex, pick a point to the left and one to the right to see how to graph the parabola.

9. Graphing Quadratic Functions
UPDATE!!!
5 Simple Steps
(make sure to identify the a, b, and c values)
Find the equation of the axis of symmetry
& draw it on the graph
Find the vertex coordinates & plot vertex on graph
Find and plot the y-intercept point
Find and plot another point on the other side of the vertex
Sketch the curve and reflect it across the
 axis of symmetry

10. A is positive 1, so the parabola opens up with (0,0) as the low point.
Graph Points
Line of symmetry
A is positive 1, so the parabola opens up with (0,0) as the low point.

11. GRAPH: y = x2-x-6 Identify the a, b, and c values
First find the vertex
Make a table with an x value to the right and left of the vertex x value
Graph these points and connect.
Label the vertex

12. Find vertex and plug in to find y. value to have high or low point.1.

13. The x value of the vertex is 1/2
Now find the y value of the vertex by plugging x back into the equation. y = x2-x-6
y = (1/2)2 – ½ - 6
The y value is -25/4.
Now pick a point to the left and right of ½.

14. y = x2-x-6
GRAPH:
I try to pick points equal distance from the vertex x value. I also tried 0 here.

15. Y=x2-x-6 Vertex low line of symmetry x = opens up (a positive)
If you pick points equal distance from the vertex, you will get the same value for y. Your graph will be symmetrical.
line of symmetry x =
opens up (a positive)

16. a is negative-opens down
Graph: y= -2x2+2x+1
a is negative-opens down
Line of Symmetry
Find the y value, then pick a point to the left and right of 1/2 to see how to draw the parabola.
= 1 2

17. 2 - - 2 - 2 - 2

18. y=-2x2+2x+1