Let f (x) = x^2 + 4x - 31. for what value of a is there exactly one real value of x such that f (x) = a?

Question

Mathematics

Emery

21 October, 02:45

Let f (x) = x^2 + 4x - 31. for what value of a is there exactly one real value of x such that f (x) = a?

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Answers (1)

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Oliver Davis · Answer 1

This value of "a" is exactly the y-coordinate of the vertex of the parabola

y = x%5E2+%2B+4x++-+31.

To find it, complete the square:

x%5E2+%2B+4x++-+31 = %28x%2B2%29%5E2+-+4+-+31 = %28x%2B2%29%5E2+-+35.

So, this value of "a" is a = - 35.

Figure. Plot y = x%5E2+%2B+4x++-+31.