Stitz-Zeager_College_Algebra_e-book

# Sometimes these values of x are called the break even

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online