Stitz-Zeager_College_Algebra_e-book

Sometimes these values of x are called the break even

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Unformatted text preview: tion x2 − 4x + 3 = 0. Factoring gives us (x − 3)(x − 1) = 0 so that x = 3 or x = 1. The x-intercepts are then (1, 0) and (3, 0). To find the y -intercept, we set x = 0 and find that y = f (0) = 3. Hence, the y -intercept is (0, 3). Plotting additional points, we get y 8 7 6 5 4 3 2 1 −1 1 2 3 4 5 x −1 f (x) = x2 − 4x + 3 From the graph, we see the domain is (−∞, ∞) and the range is [−1, ∞). The function f is increasing on [2, ∞) and decreasing on (−∞, 2]. A relative minimum occurs at the point (2, −1) and the value −1 is both the relative and absolute minimum of f . 140 Linear and Quadratic Functions 2. Note that the formula for g (x) doesn’t match the form given in Definition 2.5. However, if we took the time to expand g (x) = −2(x − 3)2 + 1, we would get g (x) = −2x2 + 12x − 17 which does match with Definition 2.5. When we find the zeros of g , we can use either formula, since both are equivalent. Using the formula which was given to us, we...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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