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CCGPS Geometry Day 37 ( ) UNIT QUESTION: How are real life scenarios represented by quadratic functions? Today’s Question: How do we graph quadratic functions in vertex form? Standard: MCC9-12.F.BF.3

3.2 Graphing Quadratic Functions in Vertex Form Graphing Using Transformations Graphing Using Transformations Domain and Range of Quadratics Domain and Range of Quadratics

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

Vertex Form Equation y=a(x-h)2+k If a is positive, parabola opens up If a is negative, parabola opens down. The vertex is the point (h,k). The axis of symmetry is the vertical line x=h. Don’t forget about 2 points on either side of the vertex! (5 points total!)

Vertex Form  Each function we just looked at can be written in the form (x – h) 2 + k, where (h, k) is the vertex of the parabola, and x = h is its axis of symmetry.  (x – h) 2 + k – vertex form EquationVertex Axis of Symmetry y = x 2 or y = (x – 0) (0, 0) x = 0 y = x or y = (x – 0) (0, 2) x = 0 y = (x – 3) 2 or y = (x – 3) (3, 0) x = 3

Example 1: Graph Analyze y = (x + 2) Analyze y = (x + 2) Step 1 Plot the vertex (-2, 1) Step 1 Plot the vertex (-2, 1) Step 2 Draw the axis of symmetry, x = -2. Step 2 Draw the axis of symmetry, x = -2. Step 3 Find and plot two points on one side, such as (-1, 2) and (0, 5). Step 3 Find and plot two points on one side, such as (-1, 2) and (0, 5). Step 4 Use symmetry to complete the graph, or find two points on Step 4 Use symmetry to complete the graph, or find two points on the left side of the vertex. the left side of the vertex.

Characteristics Graph y = -(x - 3) Graph y = -(x - 3) Domain: Domain: Range: Range:

Characteristics Graph y = 2(x + 1) Graph y = 2(x + 1) Domain: Domain: Range: Range:

Assignment Practice Worksheet