1. 5.1 Graphing Quadratic Functions Algebra 2

2. Learning Check I can graph quadratic equations of the form y = (x – h) 2 + k, and identify the vertex and the equation of the axis of symmetry of a parabola.

3. What do you have to do? I was going to go into a long explanation. However, the long and short of it—here’s what you have to do: –Axis of symmetry –Find the vertex –Choose 5 points to graph the parabola –Write the equation

4. Ex. 1: Name the vertex and axis of symmetry for the graph of each equation. y = (x + 8) 2 – 1. How is this graph different from y = x 2 Remember the format. y = (x – h) 2 + k The vertex is at (h, k), but h is opposite because the negative sign. So, if you look at the equation, the vertex should be at (-8, -1).

5. Ex. 1: Name the vertex and axis of symmetry for the graph of each equation. y = (x + 8) 2 – 1. How is this graph different from y = x 2 The axis of symmetry happens to be whatever the h is in (h, k). So in this case, h = - 8, so x = -8. It differs from the graph y = x 2 in that the vertex is translated 8 units to the left and 1 unit down.

6. Ex. 2: Name the vertex and axis of symmetry for the graph of each equation. Table of values y = (x + 1) 2 +3. Then draw the graph. The vertex is (h, k)— opposite h. (-1, 3) The axis of symmetry will be x = -1. x(x + 1) 2 +3y -4(-4 + 1) 2 +3 12 -3(-3 + 1) 2 +37 -2(-2 + 1) 2 +34 (-1 + 1) 2 +33 0(0 + 1) 2 +34 1(1 + 1) 2 +37 2(2 + 1) 2 +3 12

7. Ex. 2: Name the vertex and axis of symmetry for the graph of each equation. y = (x + 1) 2 +3. Then draw the graph. The vertex is (h, k)— opposite h. (-1, 3) The axis of symmetry will be x = -1. Notice that the points with the same y-coordinates are the same distance from the axis of symmetry, x = -1

8. Ex. 3: Write the equation of the quadratic function for each graph. The vertex of this parabola is at (-2, 0) which is (h, k) y = (x – h) 2 + k, y = (x – (-2)) 2 + 0 y = (x + 2) 2 + 0

9. Ex. 4: Write each equation in the form y = (x – h) 2 + k. Then name the vertex and the axis of symmetry. 19. f(x)= x 2 – 4x +4 (You have to factor. If you can’t recognize this yet, you are in trouble.) y = (x – 2) 2 + 0 The vertex is at (2, 0) and the axis of symmetry is at x = 2

10. Ex. 5: Write each equation in the form y = (x – h) 2 + k. Then name the vertex and the axis of symmetry. 22.f(x)= x 2 – 7 y = (x – 0) 2 – 7 The vertex is at (0, -7) and the axis of symmetry is at x = 0

11. Assignment pp. 363-364 #6-42 all

12. What do you have to do? Problems #27-42, you have to graph. You need the following: –Write the equation –Axis of symmetry –Find the vertex –Choose 5 points to graph the parabola –Graph the parabola