Goal: Graph quadratic functions in different forms

 Find the product:  (x + 6)(x + 3)  (x – 5) 2  4(x + 5)(x – 5)  Write y = x(8x + 12) + 5 in Standard form

DefinitionSteps to Graphing  y = a(x – h) 2 + k  When a>0 the parabola opens up  When a<0 the parabola opens down x = h  Step 1:Draw the axis of symmetry. It is the line x = h. (h, k)  Step 2: Plot the vertex (h, k)  Step 3:Plot two points on one side of the axis of symmetry. Use symmetry to plot two more points on the opposite side of the axis of symmetry  Step 4: Draw a parabola through the points

DefinitionSteps for Graphing  y = a(x – p)(x – q)  When a < 0 the parabola opens down  When a > 0 the parabola opens up  The graph will contain (p, 0) and (q, 0) x = p + q  Step 1: Draw the axis of symmetry. It is the line x = p + q 2 p + q  Step 2: Find and plot the vertex. The x- coordinate of the vertex is p + q 2 Substitute the x-coordinate for x in the function to find the y-coordinate of the vertex.  Step 3: Plot the points where the x- intercepts, p and q, occur.  Step 4: Draw a parabola

 Minimum Value  When a > 0  Maximum Value  When a < 0

 Tell whether the function y = -4 (x + 6)(x – 4) has a minimum value or a maximum value. Then find the minimum or maximum value.

 Tell whether the function y = ½ (x + 8) 2 – 12 has a minimum value or a maximum value. Then find the minimum or maximum value.

 Tell whether the function y = 3(x – 4)(x – 7) has a minimum value or a maximum value. Then find the minimum or maximum value.