Section 3.3

# Section 3.3 - to find the y-intercept let x = 0 Graph using...

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Section 3.3 Analyzing Graphs of Quadratic Functions A quadratic function is a 2 nd degree polynomial. f(x) = ax 2 + bx + c a, b and c are real #’s a 0 The graph of a quadratic function is a parabola. If a 0 (a is pos.) If a < 0 (a is neg.) the parabola opens up. the parabola opens down. The vertex is a minimum. The vertex is a maximum. There are 2 methods to graph a quadratic function that has an x 2 and an x term. Method 1 Complete the square, write the function in the form f(x) = a( x - h) 2 + k Graph using graphing techniques. f(x) = x 2 4x + 6 F(x) = - 2x 2 - 4x + 1 Recall to stretch vertically by a factor of 2, multiply each y-coordinate of y = x 2 by 2 Method 2 Decide if the graph opens up or down. Then find and graph the vertex, axis of symmetry and x- and y-intercepts.

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The vertex of the graph of a quadratic function, f(x) = ax 2 + bx + c is . The axis of symmetry is the vertical line, . Recall: to find the x-intercept, let y = 0,
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Unformatted text preview: to find the y-intercept let x = 0. Graph using Method 2. f(x) = -2x 2-6x + 1 Find the vertex. Determine whether there is a maximum or minimum value and find that value. Find the range. Find the intervals on which the function is increasing and the intervals on which it is decreasing. Solve. p. 273, 44. A model rocket is launched with an initial velocity of 150 ft/sec from a height of 40 ft. The function s(t) = -16t 2 + 150t + 40 gives the height of the rocket t seconds after is has been launched. Determine the time at which the rocket reaches its maximum height and find the maximum height. p. 274, 49. Classic Furniture Concepts has determined that when x hundred wooden chairs are built, the average cost per chair is given by C(x) = 0.1x 2-0.7x + 1.625, where C(x) is in hundreds of dollars. How many chairs should be built in order to minimize the average cost per chair?...
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