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Presentation transcript:

Warm Up

Graphing Quadratic Functions

Graphing Quadratic Functions Brainstorm everything you know about a quadratic function.

THE GRAPH OF A QUADRATIC FUNCTION The parabola opens up if a>0 and opens down if a<0 y = x2 The parabola is wider than the graph of y = x2 if |a| < 1 and narrower than the graph of y = x2 if |a| > 1. vertex y = -x2 Axis of symmetry

STANDARD FORM Graph y = 2x2 -8x +6 a = 2, b = -8, c = 6. Solution: The coefficients for this function Since a>0, the parabola opens up. The x-coordinate is: x = -b/2a The y-coordinate is: The vertex is a = 2, b = -8, c = 6. x = -(-8)/2(2) x = 2 y = 2(2)2-8(2)+6 y = -2 (2,-2).

GRAPH VERTEX: AXIS OF SYMMETRY: Y INTERCEPT:

VERTEX FORM OF QUADRATIC EQUATION y = a(x - h)2 + k The vertex is (h,k). The axis of symmetry is x = h.

GRAPHING A QUADRATIC FUNCTION IN VERTEX FORM Example y = -1/2(x + 3)2 + 4 VERTEX: AXIS OF SYMMETRY: Y INTERCEPT:

INTERCEPT FORM OF QUADRATIC EQUATION y = a(x - p)(x - q) The x intercepts are p and q. The axis of symmetry is halfway between (p,0) and (q,0).

GRAPHING A QUADRATIC FUNCTION IN INTERCEPT FORM Example y = -(x + 2)(x - 4). VERTEX: AXIS OF SYMMETRY: Y INTERCEPT: X INTERCEPT:

WRITING THE QUADRATIC EQUATION IN STANDARD FORM (1). y = -(x + 4)(x - 9) (2). y = 3(x -1)2 + 8 -x2 + 5x + 36 3x2 - 6x + 11