GRAPHING QUADRATIC FUNCTIONS

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Presentation transcript:

GRAPHING QUADRATIC FUNCTIONS

PROPERTIES OF A QUADRATIC FUNCTION The equation must be in standard form. y = ax2 + bx + c The graph of y = ax2 + bx + c is a parabola. If a is positive, the parabola opens up. If a is negative, the parabola opens down. The vertex has an x-coordinate of – 1b/2a. The axis of symmetry is the vertical line through the vertex.

STEP FOR GRAPHING A QUADRATIC FUNCTION: Find the x-coordinate of the vertex. (-1b/2a) Make a table of values using x- values to the left and right of the vertex (two on each side). Substitute these values into your equation to get your y-coordinates. Plot the points and connect them with a smooth curve to form a parabola.

a = 1, b = -2, c = -3 Vertex = -1b/2a EXAMPLE: Y = X2 – 2X – 3 -1(-2) 2(1) x = 2/2 = 1 X Y -1 1 2 3

Y = 3X2 – 2X – 1 X Y