QUADRATIC FUNCTIONS IN STANDARD FORM 4.1B. Review  A quadratic function can be written in the form y = ax 2 + bx + c.  The graph is a smooth curve called.

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Presentation transcript:

QUADRATIC FUNCTIONS IN STANDARD FORM 4.1B

Review  A quadratic function can be written in the form y = ax 2 + bx + c.  The graph is a smooth curve called a parabola.

Other vocabulary  Vertex  Axis of symmetry  Maximum or minimum value

Properties of the graph of y = ax 2 + bx + c  The x coordinate of the vertex is x = -b/(2a)  The y-intercept is (0,c)  If a > 0 the graph opens up, if a < 0 the graph opens down  The larger the magnitude of a, the narrower the graph

Steps for graphing quadratics in standard form  Find the coordinates of the vertex  Decide whether the graph opens up or down  Find the y-intercept  Reflect that point over the axis of symmetry  Graph one other set of points

Practice  Graph y = 2x 2 – 8x + 6  Graph y = 3x 2 + 6x + 1  Graph y = -x 2 – 4x + 2  Graph y = 1/3x 2 + 6x – 2  Graph y = x 2 + 4x