9-1 Graphing Quadratic Functions

1. 9-1 Graphing Quadratic Functions All graphs must be completed on graph paper – check out the LCMS website to download coordinate planes. Algebra 1 Glencoe McGraw-Hill Linda Stamper and JoAnn Evans

2. Quadratic Functions A quadratic function is a function that can be written in the standard form: Every quadratic function has a U-shaped graph called a parabola. y y x x The parabola opens down if the value of a is negative. The parabola opens up if the value of a is positive.

3. Will the parabola open up or down? up down Rewrite the equation in standard form first to determine the leading coefficient. down

4. The vertex is the lowest point on parabolas that open up. The vertex is the highest point on parabolas that open down. The lowest point is also known as the minimum. The highest point is also known as the maximum. y y • x x •

5. The vertical line passing through the vertex that divides the parabola into two symmetric parts is called the axis (line) of symmetry. y y • x x • axis (line) of symmetry axis (line) of symmetry

6. Each point on the parabola that is on one side of the axis of symmetry has a corresponding point on the parabola on the other side of the axis. The vertex is the only point on the parabola that is on the axis of symmetry. y y • x x • axis (line) of symmetry axis (line) of symmetry

7. GRAPHING A QUADRATIC FUNCTION 1. Find the x-coordinate of the vertex, which is 2. Make a table of values. Using x-values, calculate at least two values to the left and two values to the right of the vertex. If all of your values are on one side of the vertex, you will graph half of a parabola. 3. Plot the points and connect them with a smooth curve to form a parabola. Put arrows on the ends of the parabola. The axis of symmetry for y = ax2+ bx + c is the vertical line The y-intercept of y = ax2+ bx + c is the value given for “c”.

8. Sketch the graph of Find the x-coordinate of the vertex. (Write formula for vertex, substitute the values and simplify.) Will the parabola open up or down? What is the value of “a”? What is the value of “b”? What is the y-intercept?

9. y-intercept matchy, matchy! x y 0 -4 -2 -2 -4 1 2 3

10. y y-intercept matchy, matchy! x y 0 -4 -2 -2 -4 1 x • • • 2 • • 3 What is the equation for the axis of symmetry?

11. Copy the following on your graph paper - then graph. Example 1 Example 2 Example 3 Example 4 Example 5 Will the parabola open up or down? What is the value of “a”? What is the value of “b”? What is the y-intercept?

12. Example 1 Sketch the graph of

13. y-intercept matchy, matchy! x y -2 -5 -5 -2 -3 -2 -6 -1 0 1

14. y y-intercept matchy, matchy! x y -2 -5 -5 -2 -3 -2 x -6 -1 • • 0 1 • • • x = –1 What is the equation for the axis of symmetry?

15. Copy the following on your graph paper - then graph. Example 1 Example 2 Example 3 Example 4 Example 5

16. Example 2 Sketch the graph of: matchy, matchy! x y -4 -6 -6.25 -6 -4 -1 0 1 2 x = ½ What is the equation for the axis of symmetry?

17. Example 3 Sketch the graph of: matchy, matchy! x y -1 0 1 2 3 0 -3 -4 -3 0 x = 1 What is the equation for the axis of symmetry?

18. Example 4 Sketch the graph of: matchy, matchy! x = 0 x y -2 -1 0 1 2 -3 0 1 0 -3 What is the equation for the axis of symmetry?

19. Example 5 Sketch the graph of: matchy, matchy! x y 1 2 3 4 5 3 0 -1 0 3 x = 3 What is the equation for the axis of symmetry?

21. Homework 9-A2 Page 475-477 #16–25,63-65.