Graphing Quadratic Functions Concept A simple quadratic function

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: 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. Table of Contents

• Example 1 Face Down Face Up Table of Contents

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

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

• When graphing quadratic functions, it can be helpful to plot all intercepts. x-intercepts y-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. Table of Contents

• Example 3 x-intercepts y-intercept Table of Contents

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

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