1. Day 122 – Understanding the parts of a Quadratic with Real World Data and write the Equation 2

2. Line of Symmetry
Parabolas have a symmetric property to them. If we drew a line down the middle of the parabola, we could fold the parabola in half. We call this line the line of symmetry. Or , if we graphed one side of the parabola, we could “fold” (or REFLECT) it over, the line of symmetry to graph the other side.

3. Finding the Line of Symmetry
When a quadratic function is in standard form The equation of the line of symmetry is This is best read as … the opposite of b divided by the quantity of 2 times a.

4. Finding the Line of Symmetry
For example… Find the line of symmetry of Using the formula … Thus, the line of symmetry is x = 3.

5. Finding the Vertex
We know the line of symmetry always goes though the vertex. Thus, the line of symmetry gives us the x- coordinate of the vertex. To find the y-coordinate of the vertex, we need to plug the x-value into the original equation.

6. Step 1: Find the line of symmetry
Finding the Vertex
Step 1: Find the line of symmetry

7. Finding the Vertex
Step 2: Plug the x – value into the original equation to find the y-value. Therefore, the vertex is (2,5)

8. Example
1) Domain: Range: Vertex: Max or min: x-intercepts: Axis of symmetry ___________

9. Example
1) Domain: x = ℝ Range: y ≤ 4 Vertex: (0,4) Max or min: max x-intercepts: –2,2 Axis of symmetry x = 0

10. 2) Domain: Range: Vertex: Max or min: x-intercepts: Axis of symmetry
Example
2) Domain: Range: Vertex: Max or min: x-intercepts: Axis of symmetry

11. Example
2) Domain: x = ℝ Range: y ≤ 9 Vertex: (–1,9) Max or min: max x-intercepts: –4,2 Axis of symmetry x = –1

12. 3) Domain: Range: Vertex: Max or min: x-intercepts: Axis of symmetry
Example
3) Domain: Range: Vertex: Max or min: x-intercepts: Axis of symmetry

13. Example
3) Domain: x = ℝ Range: y ≥ –1 Vertex: (0, – 1) Max or min: min x-intercepts: –1,1 Axis of symmetry x = 0

14. Word Problems The quadratic function
f(x) = x2 is graphed at the right.
In which direction does the graph open?
Why is the graph located in Quadrants I and II?
Graph the function
In which directions does the graph open?
In which quadrants is the graph located?
What must you do to the graph of f to obtain the graph of g?

15. Word Problems - Answers
The quadratic function
f(x) = x2 is graphed at the right.
In which direction does the graph open? up
Why is the graph located in Quadrants I and II?
Squared x values produce positive y-values, y-values y are positive only in Quadrants I and II.
3. Graph the function

16. Word Problems - Answers
In which directions does the graph open?
Down
5. In which quadrants is the graph located?
Quadrants III and IV
What must you do to the graph of f to obtain the graph of g?
Reflect it over the x-axis

17. Word Problems
7. Graph f(x) = x2, p(x) = x2 + 1 and q(x) = x2 – 2 on the same set of axes. 8. Where is the graph of p in relation to the graph of f? 9. Where is the graph of q in relation to the graph of f?

18. Word Problems - answers
7. Graph f(x) = x2, p(x) = x2 + 1 and q(x) = x2 – 2 on the same set of axes. 8. Where is the graph of p in relation to the graph of f? up 1 unit 9. Where is the graph of q in relation to the graph of f? Down 2 units