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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
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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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