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SFM Productions Presents: Another joyous day continuing your Pre-Calculus experience! 2.1Quadratic Functions and Models

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Homework for section 2.1 p1327-12 (all), 21-33 (eoo), 35- 45, 49-55, 65, 71, 73, 76, 81, 84 The last three word problems are important; I will check to make sure you did them - penalties will be assessed as needed.

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We are going to be looking at graphs of polynomial functions. Called a polynomial function with degree n. If n=0, then you have a constant function. If n=1, then you have a linear function. y = 3 y = 4x+3 If n=2, then you have a quadratic function.

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Quadratic functions can look like any of these:

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Quadratic equations have an: axis of symmetry X = 0 X = -2X = 6

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Quadratic equations have: vertices, or in the singular: a vertex Vertex is a minimum Vertex is a maximum

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Remember Vertical & Horizontal Shifts? Remember: Stretching Shrinking ??

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The STD form of a Quadratic Equation: What is (h,k)? Vertex: (h,k) Graph (without your battery operated brain for now … ) YOUR PAL AND MINE! Completing the Square X-intercepts: ?

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Try another … V = (3, 1) and x-intercepts are: (4, 0) and (2, 0)

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Another:Find an equation of a parabola that has a V = (1, 2) and passes through the origin.

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Another:Find an equation of a parabola that has a V = (2, 3) and passes through (0, 2).

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An easier way to find the vertex of a parabola: (x, y) (x, f(x))

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A baseball is hit at a point 3 feet above the ground at a velocity of 100 fps at 45 o. The path of the ball is given by the following function: (Where f(x) is the height in ft, and x is the distance in feet.) What is the maximum height of the ball? What is the distance from the batter when the ball hits the ground? What is the distance from the batter when the ball is at a height of 3 feet?

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Go! Do!

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

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

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