1. 9.2 Graphing Quadratic Equations
Algebra 1

2. Quadratic function Standard form
Every quadratic function has a U-shaped graph called a parabola.
Vertex is the lowest or highest pt of the parabola.
Axis of symmetry – line passing thru the vertex, dividing the U in half.

3. Graph of a Quadratic function

4. Steps to graph a quadratic f(x)
1) Use to find half of the vertex and axis of symmetry.
2) Substitute the x value into the equation to find the y value of the vertex.
3) Use the vertex to make your T-chart to find 4 other points on the parabola.

5. Example 1
Solve by graphing.
1.) 2.) Substitute
3.) T-chart

6. Graph of Ex. 1

7. Ex. 2
#63 on pg. 522

8. Graph of Ex. 2

9. Assignment

10. Example 1, Step 3
x l y
-2 l
-1 l
0 l
1 l
2 l

11. Example 1 – Substitute each value into the equation.
x l y
-2 l -8
-1 l
0 l
1 l
2 l

12. Example 1- Substitute -1
x l y
-2 l –8
-1 l –9
0 l
1 l
2 l

13. Example 1 – Substitute 0
x l y
-2 l –8
-1 l –9
0 l –8
1 l
2 l

14. Example 1 – Substitute 1
x l y
-2 l –8
-1 l –9
0 l –8
1 l –5
2 l

15. Example 1 – Substitute 2
x l y
-2 l –8
-1 l –9
0 l –8
1 l –5
2 l 0

16. Example 1
Did you see that we had a zero as the y value on our last point, (2,0)? This is one of the roots or zero’s. Once, you graph it you should see that the parabola also crosses the x-axis at –4. Which is the other answer we found when factoring. I hope that you can graph this example on graph paper to see what I am referring to. Good Luck!

17. A quadratic equation…
is an equation in which the value of the related quadratic function is 0.

18. Example 1
Solve by Factoring
(x+4)(x-2)=0
x+4=0 x-2=0
x= x=2

19. Roots and Zero’s
For example, We have used factoring to solve for x or the “roots”. The x values are the x-intercepts or the “zero’s” of the equation. They are called the “zero’s” because the y value is zero in the ordered pair. Let’s find the zero’s of this example.