Graph Quadratic Functions in Standard Form

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Presentation transcript:

Graph Quadratic Functions in Standard Form Notes 4.1 (Day 2) Graph Quadratic Functions in Standard Form

Graphing any quadratic (x2) function, The a value: The graph will hold water if a > 0, and will spill water if a < 0. The graph is more narrow than the parent function if a > 1 or a < -1 . The graph is wider than the parent function if -1 < a < 1 .

With a, finds the x coordinate of the vertex The b value: With a, finds the x coordinate of the vertex To find the x – coordinate of the vertex: IMPORTANT!!!

The c value: - This value shifts the graph up and down

Vertex: Is either the minimum or maximum value of a parabola The x coordinate of the vertex also determines where the axis of symmetry lies.

Maximum and Minimum Values: The vertex will be the maximum or minimum value. If the parabola holds water, it will be a minimum value. If the parabola spills water, it will be a maximum value.

Axis of Symmetry Divides the parabola into mirror images and passes through the vertex. Is literally the equation x = (it will be a vertical line for all parabolas)

How to graph a quadratic in the form Step 1: Find the x – coordinate of the vertex. Step 2: Make a t-chart of 5 values, with the middle x value being the x – coordinate of the vertex. Step 3: The four missing values in your t-chart will be the first two integers on either side of the x-coordinate of the vertex. Step 4: Solve for the y – values. Step 5: Plot the points and connect the dots. Step 6: Label the min. or max. and the axis of symmetry (dotted line)

Example: Graph the Quadratic Function. b = c =

Example: Graph the Quadratic Function. b = c =

Example: Graph the Quadratic Function. b = c =

Homework: Graphing Quadratics (Parabolas) Worksheet