Question

Graph both functions to find the solution(s) to the system. {f(x)=x+1 g(x)=x2−6x−7   Use the line tool to graph the line. Use the parabola tool to graph the parabola. Choose maximum or minimum point first and then a point on the parabola.

Answer 1

For the line, plot the points: ( 8, 9 ) & ( -1, 0 )

For the parabola, plot the points: ( 3, 16 ) & ( 8, 9 )

This is the correct answer! I just took the test!! Good luck!

Answer 2

solutions to f(x)=g(x) are x=-1 and x=8

Explanation:

The minimum point of the parabola will be found at ...

x = -b/(2a) . . . . . where a, b, c are the coefficients of ax²+bx+c

For g(x) = x² -6x -7, the minimum will be at x=-(-6)/(2·1) = 3. The minimum value is ...

g(3) = 3² -6·3 -7 = -16

so the vertex (minimum point) you want to plot is (3, -16). Since the coefficient of x² is 1, there is no vertical scaling, so when the value of x differs from 3 by 1 unit, the value of g(x) will be 1² = 1 unit higher. That is, g(4) = -15, so (4, -15) is another point on the parabola.

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I find it convenient to use a graphing calculator for the whole problem.