5.1 Graphing Quadratic Functions Copy the notes from each slide of this power point into your notes section, including graphs. Complete the in-class practice.

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Presentation transcript:

5.1 Graphing Quadratic Functions Copy the notes from each slide of this power point into your notes section, including graphs. Complete the in-class practice assigned. Finish for homework. Both notes and homework will be checked tomorrow.

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. Example quadratic equation:

Vertex- The maximum or minimum point of a parabola. Vertex Axis of symmetry- The vertical line through the vertex of the parabola. Axis of Symmetry

Standard Form Equation y=ax 2 + bx + c If a is positive, the parabola opens up If a is positive, the parabola opens up If a is negative, the parabola opens down The x-coordinate of the vertex is at x = The x-coordinate of the vertex is at x = To find the y-coordinate of the vertex, plug the x- coordinate into the given equation. To find the y-coordinate of the vertex, plug the x- coordinate into the given equation. 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 equation to find the corresponding y-values. Choose 2 x-values on either side of the vertex x- coordinate. Use the equation 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.

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 vertical line x=2 Table of values for otherTable of values for other points: choose x’s next to points: choose x’s next to vertex vertex x y x y * Graph! * Graph! x=2

Now you try one! y=-x 2 +4x-2 * Open up or down? * Vertex? * Axis of symmetry? * Table of values with 5 points?

Zeros

To Write a Quadratic Function in Standard Form: - Use FOIL or distributive property to eliminate the parenthesis - Then, combine like terms.

In Class Practice and Finish for Homework: Page 253 – 254 #4, 5, 7, 10-15; Problems that need to be graphed should be completed on graph paper! All work and calculations need to be shown!