Steps 4 and 5: Find additional points, plot the points, and sketch the graph. To plot the x-intercepts, we can either approximate them by hand or use a calculator. x y 5 (1 √3, 0) (1 √3, 0) 5 5 y x2 2x 2 5 Vertex (1,3) x y 1 3 0 2 1 13 2.7 0 1 13 0.7 0 2 2 Vertex S y-int. S x-int. S x-int. S YOU TRY 4 Graph y x2 8x 14. Notice in Example 3, y x2 4x 3, the value of a is negative (a 1) and the parabola opens downward. In Example 4, the graph of y x2 2x 2 opens upward and a is positive (a 1). This is another characteristic of the graph of y ax2 bx c. If a is positive, the graph opens upward. If a is negative, the graph opens downward. Using Technology In Section 7.5, we said that the solutions of the equation x2 x 6 0 are the x-intercepts of the graph of y x2 x 6. The x-intercepts are also called the zeros of the equation since they are the values of x that make y 0. We can fi nd the x-intercepts shown on the graphs by pressing 2nd TRACE and then selecting 2: zero. Move the cursor to the left of an x-intercept using the right arrow key and press ENTER. Move the cursor to the right of the x-intercept using the right arrow key and press ENTER. Move the cursor close to the x-intercept using the left arrow key and press ENTER. The result fi nds the x-intercepts (2, 0) and (3, 0) as shown on the graphs below. The y-intercept is found by graphing the equation and pressing TRACE 0 ENTER. As shown on the graph at the left below, the y-intercept for y x2 x 6 is (0, 6). The x-value of the vertex can be found using the vertex formula. In this case, a 1 and b 1, so b 2a 1 2 . To fi nd the vertex on the graph, press TRACE, type 1/2, and press ENTER. The vertex is shown as (0.5, 6.25) on the graph in the center below. 636 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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