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Section 5.1 – Graphing Quadratics

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REVIEW Graphing

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Big Question… Are lines the only type of graph? Hhhmmm…what would Lisa say? I GOT IT!

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Some other types… Have you seen these before?

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Going a little farther… What else could graphs look like?

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Graphing a curve.. Is it possible that the certain equations when graphed will give us a curve? YES Is it possible that other certain equations give us neither a straight line or a curve, but something else totally different? YES

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Section 5.1 – Graphing a Quadratic Equation Quadratic Equation: trinomial function defined by the form y = ax 2 + bx + c. Examples: y = x 2 + 4x + 5 y = 9x 2 + 16x y = - 4x 2 - 11

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Section 5.1 – Graphing a Quadratic Equation Three Parts of a Quadratic Equation: y = ax 2 + bx + c Lead CoefficientLinear Coefficient Constant Quadratic Term Linear Term

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Section 5.1 – Graphing a Quadratic Equation Parabola: graph of any quadratic term, which is a smooth continuous curve. (Shaped like a "U") Vertex: Point on the parabola where the curve and axis of symmetry intersect. Also the local maximum and local minimum of the graph as well. Point where the direction of graph changes.

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Section 5.1 – Graphing a Quadratic Equation Axis of Symmetry: Center line of a parabola, splits the parabola into two symmetrical halves.

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Section 5.1 – Graphing a Quadratic Equation Zeros of a Function: points (coordinates) where the curve intersects the x-axis. Roots of a Quadratic Function: values of the variable that satisfy the quadratic equation.

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Section 5.1 – Graphing a Quadratic Equation Base Quadratic Function y = x 2 Vertex Axis of Symmetry

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Section 5.1 – Graphing a Quadratic Equation Domain of Base Quadratic Function: ALL REAL NUMBERS Range of Base Quadratic Function: { y | y > 0 }

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5.1 Modeling Data with Quadratic Functions. Quadratic Function: f(x) = ax 2 + bx + c a cannot = 0.

5.1 Modeling Data with Quadratic Functions. Quadratic Function: f(x) = ax 2 + bx + c a cannot = 0.

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