8.4 Graphing.

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Presentation transcript:

8.4 Graphing

Axis of Symmetry

Vertex Coordinate (x,y) The x coordinate is x= -b/(2a) Plug in the axis of symmetry for x into the equation and find the corresponding y value

Steps to Graph a Quadratic Draw the Axis of Symmetry Plot the Vertex (x,y) Determine width of parabola: Find x intercepts (roots or zeros) if factorable. If not factorable use x, y chart . For the x, y chart pick the x value from your axis of symmetry and 2 x-values less than your axis of symmetry and 2 x-values greater than your axis of symmetry. Plot the y- intercept (which is c) Label Domain and Range

Graph A = -2 B = +4 C = 1

Graph x y 3 -5 2 1 -1 x y 3 2 1 -1 Axis of symmetry is x= 1 Vertex: y= -2(1)² + 4(1) +1 y= -2 +4+1 y = 3 Vertex : (1, 3) x y 3 -5 2 1 -1 x y 3 2 1 -1 X-intercepts 0 = -2x² +4 +1 0= not factorable as of now so use a xy chart

Graph x y 3 -5 2 1 -1 x y 3 2 1 -1

the range is y> the y coordinate of the vertex When a<0 Domain (x) Range (y) All Real Numbers When a>0 the range is y> the y coordinate of the vertex When a<0 the range is y< the y coordinate of the vertex

Domain is all real numbers Graph x y 3 -5 2 1 -1 x y 3 2 1 -1 Domain is all real numbers Range: { y | y }

Graph x y 3 2 -3 1 -4 -1 x y 3 2 1 -1 Range: { y | y } x - intercepts

Minimum and Maximum Points Vertex Maximum if a<0 (negative) Minimum if a>0 (positive)

Free Graphing Calculator Online www.desmos.com