Rewrite the function by completing the square. f(x)=x^{2}+14x+64

Question

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Answer 1

x^2 + 14x + 64

take half of 14, 14/2 = 7 and square it, 7^2 to get 49

add and subtract 49. If you add & subtract the same thing, you leave the expression with the same value

= (x^2 + 14x + 49) + (64 -49)

factor the 1st parentheses, as it's a perfect square (x+7)^2 = x^2 + 14x +49

= (x+7)^2 +25

f(x) = (x+7)^2 + 25

general equation for an upward opening parabola is

y = f(x) = (x-h)^2 + k where (h,k) is the vertex

In the given problem (h,k) = (-7,25) = vertex or minimum point