Definition/Procedure Example A woman dives off of a cliff 49 m above the ocean. Her height, h(t), in meters, above the water is given by h(t) 9.8t2 49 where t is the time, in seconds, after she leaves the cliff. When will she hit the water? Let h(t) 0, and solve for t. h(t) 9.8t2 49 0 9.8t2 49 Substitute 0 for h. 9.8t2 49 Add 9.8t2 to each side. t2 5 Divide by 9.8. t 15 Square root property Since t represents time, we discard 15. She will hit the water in 15, or about 2.2, sec. Solving Application Problems Using a Quadratic Equation. (p. 649) 10.5 Quadratic Functions and Their Graphs A quadratic function is a function that can be written in the form f (x) ax2 bx c, where a, b, and c are real numbers and a 0. The graph of a quadratic function is called a parabola. The lowest point on an upward-opening parabola or the highest point on a downward-opening parabola is called the vertex. (p. 653) A quadratic function can also be written in the form f (x) a(x h)2 k: 1) The vertex of the parabola is (h, k). 2) The axis of symmetry is the vertical line with equation x h. 3) If a is positive, the parabola opens upward. If a is negative, the parabola opens downward. 4) If 0 a 0 1, then the graph of f (x) a(x h)2 k is wider than the graph of y x2. If 0 a 0 1, then the graph of f (x) a(x h)2 k is narrower than the graph of y x2. (p. 657) f (x) 5x2 7x 9 is a quadratic function. Graph f (x) (x 3)2 4. x y x3 V(3, 4) 5 5 5 5 f(x)(x 3)2 4 Vertex: (3, 4) Axis of symmetry: x 3 a 1, so the graph opens downward. The domain is (q, q); the range is (q, 4. 694 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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