9 3 Graphing Quadratic Functions Objective Graph a
9 -3 Graphing Quadratic Functions Objective Graph a quadratic function in the form y = ax 2 + bx + c. Holt Mc. Dougal
9 -3 Graphing Quadratic Functions Step 1 Find the axis of symmetry. Step 2 Find the vertex. Step 3 Find the y-intercept. Step 4 Find two more points on the same side of the axis of symmetry as the point containing the y-intercept. Step 5 Graph the axis of symmetry, the vertex, the point containing the y-intercept, and two other points. Step 6 Reflect the points across the axis of symmetry. Connec the points with a smooth curve. Holt Mc. Dougal
9 -3 Graphing Quadratic Functions Example 1 Graph y = 3 x 2 – 6 x + 1. Holt Mc. Dougal
9 -3 Graphing Quadratic Functions Helpful Hint Because a parabola is symmetrical, each point is the same number of units away from the axis of symmetry as its reflected point. Holt Mc. Dougal
9 -3 Graphing Quadratic Functions Example 2 Graph the quadratic function. y = 2 x 2 + 6 x + 2 Holt Mc. Dougal
9 -3 Graphing Quadratic Functions Example 3 Graph the quadratic function. y + 6 x = x 2 + 9 Holt Mc. Dougal
9 -3 Graphing Quadratic Functions Remember! The vertex is the highest or lowest point on a parabola. Therefore, in the example, it gives the maximum height of the basketball. Holt Mc. Dougal
9 -3 Graphing Quadratic Functions Example 4 The height in feet of a basketball that is thrown can be modeled by f(x) = – 16 x 2 + 32 x, where x is the time in seconds after it is thrown. Find the basketball’s maximum height and the time it takes the basketball to reach this height. Then find how long the basketball is in the air. Holt Mc. Dougal
9 -3 Graphing Quadratic Functions Example 5 As Molly dives into her pool, her height in feet above the water can be modeled by the function f(x) = – 16 x 2 + 16 x + 12, where x is the time in seconds after she begins diving. Find the maximum height of her dive and the time it takes Molly to reach this height. Then find how long it takes her to reach the pool. Holt Mc. Dougal
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