Question

Complete the square to identify the vertex of y=x2−16x+14 .(1 point) Responses (8,30) left parenthesis 8 comma 30 right parenthesis (8,−50) left parenthesis 8 comma negative 50 right parenthesis (8,14) left parenthesis 8 comma 14 right parenthesis (8,78)

Answer 1

To complete the square, we need to rewrite the quadratic equation in the form (x-h)^2 + k.

Given equation: y = x^2 - 16x + 14

To complete the square, we need to take half of the coefficient of x (-16) and square it:

16/2 = 8
8^2 = 64

Now, we add and subtract 64 in the equation:

y = x^2 - 16x + 14 + 64 - 64

This can be simplified as:

y = (x^2 - 16x + 64) + 14 - 64
y = (x - 8)^2 - 50

Comparing this with the form (x-h)^2 + k, we see that the vertex is (8, -50).

Therefore, the correct answer is:
(8, -50)