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Question: Solve by graphing the related function of the equation - x2 + 9x - 20 = 0.
A ) - 4 and 5
B ) 4 and 5
C ) - 5 and - 4
D ) no solution
Steps to derive
1 - x2 + 9x - 20 = 0 can be written in standard form as y = - x2 + 9x - 20.
2 Sketch the graph of the quadratic function y = - x2 + 9x - 20 as:
3 From the graph, the x-intercepts are 4 and 5.
[Estimate the values of the x-intercepts.]
4 - (4)2 + 9(4) - 20 = 0
[Substitute the x-intetcept = 4 in the equation - x2 + 9x - 20 = 0.]
5 0 = 0
[Simplify.]
6 - (5)2 + 9(5) - 20 = 0
[Substitute the x-intetcept = 5 in the equation - x2 + 9x - 20 = 0.]
7 0 = 0
[Simplify.]
8 Both the values satisfy the equation. So, 4 and 5 are the solutions of the equation.
Hence the right answer is Option B
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