Stitz-Zeager_College_Algebra_e-book

The y 1 intercept is found by setting x 0 0 6 to nd

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Unformatted text preview: ∞, 3] and decreasing on [3, ∞). The relative maximum occurs at the point (3, 1) with 1 being both the relative and absolute maximum value of g . Hopefully the previous examples have reminded you of some of the basic characteristics of the graphs of quadratic equations. First and foremost, the graph of y = ax2 + bx + c where a, b, and c are real numbers with a = 0 is called a parabola. If the coefficient of x2 , a, is positive, the parabola opens upwards; if a is negative, it opens downwards, as illustrated below.1 vertex vertex a>0 a<0 Graphs of y = ax2 + bx + c. The point at which the relative minimum (if a > 0) or relative maximum (if a < 0) occurs is called the vertex of the parabola. Note that each of the parabolas above is symmetric about the dashed vertical line which contains its vertex. This line is called the axis of symmetry of the parabola. As you may recall, there are two ways to quickly find the vertex of a parabola, depending on which form we are given. The results are summarized below. Equation 2.4. Vertex Formulas for Quadratic Functions: Suppose a, b, c, h, and k are real numbers with a = 0. • If f (x) = a(x − h)2 + k , the vertex of the graph of y = f (x) is the point (h, k ). • If f (x) = ax2 + bx + c, the vertex of the graph of y = f (x) is the point − b ,...
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