1. Homework

2. Quadratic Function A function of the form y=ax 2 +bx+c where a≠0 making a u-shaped graph called a parabola. A function of the form y=ax 2 +bx+c where a≠0 making a u-shaped graph called a parabola.

3. Vertex- The lowest or highest point of a parabola. Vertex Axis of symmetry- The vertical line through the vertex of the parabola. Axis of Symmetry

4. Standard Form Equation y=ax 2 + bx + c If a is positive, u opens up If a is positive, u opens up If a is negative, u opens down The x-coordinate of the vertex is at The x-coordinate of the vertex is at To find the y-coordinate of the vertex, plug the x- coordinate into the given eqn. To find the y-coordinate of the vertex, plug the x- coordinate into the given eqn. The axis of symmetry is the vertical line x= The axis of symmetry is the vertical line x= Choose 2 x-values on either side of the vertex x- coordinate. Use the eqn to find the corresponding y- values. Choose 2 x-values on either side of the vertex x- coordinate. Use the eqn to find the corresponding y- values. Graph and label the 5 points and axis of symmetry on a coordinate plane. Connect the points with a smooth curve. Graph and label the 5 points and axis of symmetry on a coordinate plane. Connect the points with a smooth curve.

5. Example 1: Graph y=2x2-8x+6 a=2 Since a is positive the parabola will open up. Vertex: use b=-8 and a=2 Vertex is: (2,-2) Axis of symmetry is the vertical line x=2 Table of values for other points: x yTable of values for other points: x y 06 06 10 10 2-2 2-2 30 30 46 46 * Graph! x=2

6. Now you try one! y=-x 2 +x+12 * Open up or down? * Vertex? * Axis of symmetry? * Table of values with 5 points?

7. x-(x) 2 +2x-1 y(x, y) 

8. Tell whether the graph opens up or down. Graph each using a T-chart. Find the axis of symmetry &  vertex . Use a dotted line to graph the axis of symmetry. xx 2 - 6x + 5 y(x, y) 

9. x-(x) 2 - 2x+3 y(x, y) 

10. x(x) 2 +2x-6 y(x, y) 

11. x(x) 2 +8x+13 y(x, y) 

12. Vertex Form Equation y=a(x-h)2+k + (positive)- (negative) aOpens upOpens down hMoves to the leftMoves to the right kMoves upMoves down Vertex: (h, k) *take the opposite of “h” and keep “k” the same

13. Example 2: Graph and describe transformations y=-.5(x+3) 2 +4 a is negative (a = -.5), so parabola opens down. a is negative (a = -.5), so parabola opens down. Vertex is (h,k) or (-3,4) Vertex is (h,k) or (-3,4) Axis of symmetry is the vertical line x = -3 Axis of symmetry is the vertical line x = -3 Table of values x y Table of values x y -1 2 -1 2 -2 3.5 -2 3.5 -3 4 -3 4 -4 3.5 -4 3.5 -5 2 -5 2 Vertex (-3,4) (-4,3.5) (-5,2) (-2,3.5) (-1,2) x=-3

14. Now you try one! Describe tranformations y=2(x-1) 2 +3 Open up or down? Open up or down? Vertex? Vertex? Axis of symmetry? Axis of symmetry? Table of values with 5 points? Table of values with 5 points?