Answer:
(x + 2)^2 - 11.
Step-by-step explanation:
f(x) = x^2 + 4x - 7
Now x^2 + 4x = (x + 2)^2 - 4 so we have:
f(x) = (x + 2)^2 - 4 - 7
f(x) = (x + 2)^2 - 11.
Here, we are required to express x² + 4x - 7 in the form (x+a)² - b and determine the values of a and b.
By completing the square method;
a = (4/2) = 2.
Therefore, by expanding (x+a)² i.e (x+2)²
We therefore have; x² + 4x + 4
However, the question is given as x²+4x-7
Therefore, by comparison between;
x² + 4x + 4 and x²+4x-7; we have;
4 - b = -7, b = 7+4
Ultimately, b = 11
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