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Published byLoren Fitchett Modified about 1 year ago

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Quadratic graphs Today we will be able to construct graphs of quadratic equations that model real life problems

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The Graph of a Quadratic Function All parabolas are symmetric with respect to a line called the axis of symmetry. The point where the axis intersects the parabola is the vertex of the parabola. Leading coefficient is positive. Leading coefficient is negative.

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Leading Coefficient 3 The leading coefficient of ax 2 + bx + c is a. When the leading coefficient is positive, the parabola opens upward and the vertex is a minimum. When the leading coefficient is negative, the parabola opens downward and the vertex is a maximum. x y f(x) = ax 2 + bx + c a > 0 opens upward vertex minimum x y f(x) = ax 2 + bx + c a < 0 opens downward vertex maximum

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Axis of symmetry Formula for: We can also trace to it on the graphing calculator!

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Vertex of a Parabola 5 Example: Find the vertex of the graph of f (x) = x 2 – 10x f (x) = x 2 – 10x + 22 original equation a = 1, b = –10, c = 22 The vertex of the graph of f (x) = ax 2 + bx + c (a 0) At the vertex, So, the vertex is (5, -3).

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Example: Basketball 6 Example: A basketball is thrown from the free throw line from a height of six feet. What is the maximum height of the ball if the path of the ball is: The path is a parabola opening downward. The maximum height occurs at the vertex. Find the maximum height of the ball.

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Example: Basketball 7 Example: A basketball is thrown from the free throw line from a height of six feet. What is the maximum height of the ball if the path of the ball is: The path is a parabola opening downward. The maximum height occurs at the vertex. At the vertex, So, the vertex is (9, 15). The maximum height of the ball is 15 feet.

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Graph the following path of a ball Y=-x 2 +6x Find the Max height After how Seconds does the ball hit the ground.

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Plot the points Max height is 9 The ball hits the ground After 6 seconds HEIGHTHEIGHT SECONDS

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THINGS TO KEEP IN MIND WHEN GRAPHING CHANGE THE VIEWING WINDOW BY CHANGING THE Y MIN AND Y MAX. REMEMBER THAT HEIGHT IS THE VERTICAL AXIS AND TIME IS THE HORIZONTAL AXIS

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