4.1 Graphing Quadratic Functions Alg. II

Quadratic Function A function of the form y=ax2+bx+c where a≠0 making a u-shaped graph called a parabola. Example quadratic equation:

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

Standard Form Equation y=ax2 + bx + c If a is positive, u opens up If a is negative, u opens down The x-coordinate of the vertex is at 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= 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.

Example 1: Graph y=2x2-8x+6 Axis of symmetry is the vertical line x=2 Table of values for other points: x y 0 6 1 0 2 -2 Min. or Max? 3 0 4 6 * Graph! a=2 Since a is positive the parabola will open up. Vertex: use b=-8 and a=2 Vertex is: (2,-2) x=2

Now you try one. y=-x2+x+12. Open up or down. Vertex. (1/2 , 12 ¼) Now you try one! y=-x2+x+12 * Open up or down? * Vertex? (1/2 , 12 ¼) * Axis of symmetry? x=1/2 * Table of values with 5 points? Is vertex Min. or Max.? x y -1 10 12 1/2 12 1/4 1 2

Assignment