Make the given changes in the indicated examples of this section and then solve the resulting problems. In Example 3,
Make the given changes in the indicated examples of this section and then solve the resulting problems.
In Example 3, change the − sign before 8x to + and then sketch the graph.
Data from Example 3
For the graph of the function y = 2x2 − 8x + 6, find the vertex and y-intercept and sketch the graph. (This function was also used in Example 2.) First, a = 2 and b = −8. This means that the x-coordinate of the vertex is
and the y-coordinate is y = 2(22) − 8(2) + 6 = −2
Thus, the vertex is (2, −2). Because a > 0, it is a minimum point. Because c = 6, the y-intercept is (0, 6).
We can use the minimum point (2, −2) and the y-intercept (0, 6), along with the fact that the graph is a parabola, to get an approximate sketch of the graph. Noting that a parabola increases (or decreases) away from the vertex in the same way on each side of it (it is symmetric with respect to a vertical line through the vertex), we sketch the graph in Fig. 7.14. It is the same graph as that shown in Fig. 7.13(a).
This problem has been solved!
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