1. Warm-Up
Solve the following quadratic equations

2. Homework

3. Still do not get how to solve quadratic equations?
Let’s take 10 minutes to do the scavenger hunt for more practice.

4. Lesson: Graphing Quadratic Equations
February 17, 2014

5. Recall………Quadratic Equations
So far we have learned…
What a quadratic equation is
How a quadratic equation is shaped
What the parent equation of a quadratic equation looks like
How we can transform(move) quadratic equations
and
How to solve quadratic equations

6. More on Quadratic Equations
In today's lesson we will discuss more features of the quadratic equation and how to find them such as Axis of Symmetry, and tomorrow we will learn how to graph a quadratic equation.

7. How does it look? We know that the Quadratic Parent Equation is ?
We also know that the shape of the graph of a quadratic equation is a ______________?
If you fold the parabola in half to get two equal sides. The line splitting the two halves is called the axis of symmetry
Later in this lesson we will introduce a formula for the Axis of Symmetry

8. Examining the Graph of a Parabola
Fill in the Blanks
We have learned that the ____________and the Max/Min are the same point.
If asked for the Max/Min value that would be the________________________.
The Axis of symmetry is the x-coordinate of the Vertex(Max/Min).

9. Before we can start to graph here is a visual of all the things you need to know

10. Parts of the Graph Vertex: Max or min value: the y-value of the vertex
Highest point (maximum)
Lowest point (minimum)
Max or min value: the y-value of the vertex
Axis of symmetry: the x-value of the vertex

11. Info from equation Direction of opening:
If a>0, the direction of opening is UP and the vertex would be a minimum.
If a<0, the direction of opening is DOWN and the vertex would be a maximum.
Example: y = 5x2 + 10x – 7

12. Info from equation
Y-intercept: in standard form, c gives us the y-intercept.
y = ax2 + bx + c
Example: y = 5x2 + 10x – 7

13. Give the direction of opening and y-intercept of the following:
y = -8x2 + 2x + 1
y = 6x2 – 24x - 4

14. Practice

15. How can we find the vertex of a parabola if we are not given a graph?

16. This is where the Axis of Symmetry comes in!
Recall - The line splitting the two halves of a parabola is called the axis of symmetry and the A.O.S is the x-coordinate of the Vertex(Max/Min).
So if we know the x-coordinate then we can plug that into our equation to get the y coordinate

17. Using the Axis of Symmetry
Formula for the AOS:
Always starts with x =
This indicates that it is a vertical line
Will always be x = #

18. Find the Axis of symmetry for the following quadratic equations
1) y = x2 – 2x – a = ____, b = ____, c = ____
2) y = -2x2 + 8x – a = ____, b = ____, c = ____
3) y = -x2 + 2x a = ____, b = ____, c = ____

19. Now let’s use those same problems to find the Vertex.
1) y = x2 – 2x – 3 x = ____ Vertex: ( , ) 2) y = -2x2 + 8x – 5 3) y = -x2 + 2x + 2

20. Can this be done using the calculator?
Yes
Let’s find the vertex of the following quadratic equation and state whether it is a maximum point or minimum point.

21. More Practice Using the Calculator
Find the vertex of the following quadratic equations and state whether it is a maximum point or minimum point.

22. Homework
Finding the Axis of Symmetry and Vertex using A.O.S