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Table of Contents Graphing Quadratic Functions – Concept A simple quadratic function is given by The graph of a quadratic function in called a parabola. Here is the graph of a very basic quadratic function:

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Table of Contents The value of the coefficient a determines the direction the parabola faces. When a is positive, the parabola faces up. When a is negative, the parabola faces down.

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Table of Contents Example 1 Face Up Face Down

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Table of Contents The vertex of a parabola is the lowest point (minimum y-value) on the graph of a parabola … Vertex Minimum Maximum … or the highest point (maximum y-value) on the graph.

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Table of Contents The axis of symmetry of a parabola is the vertical line going through the vertex. Notice the symmetry of the two branches of the parabola about the axis. Example 2 Draw the axis through the vertex.

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Table of Contents The equation of the axis of symmetry is given by In this case, the equation of the axis of symmetry is given by:

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Table of Contents When graphing quadratic functions, it can be helpful to plot all intercepts. x-interceptsy-intercepts Set y = f (x) = 0 and solve for x. Set x = 0 and solve for y. This is where the graph intersects the x-axis. This is where the graph intersects the y-axis.

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Table of Contents x-intercepts Example 3 y-intercept

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Table of Contents SUMMARY Axis of symmetry: Graphs of Quadratic Functions The graph of a quadratic function in called a parabola. The maximum or minimum y-value of a quadratic occurs at the vertex. Face UpFace Down x-int: y = f (x) = 0 and solve for x. y-int: x = 0 and solve for y.

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Table of Contents

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