Complete the square to identify the vertex of y=x2−16x+14
To complete the square, we need to rewrite the equation in the form of y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
For the given equation y = x^2 - 16x + 14:
Step 1: Group the x terms.
y = (x^2 - 16x) + 14
Step 2: Take half of the coefficient of x and square it. Add and subtract this value within the parentheses.
y = (x^2 - 16x + (-16/2)^2) + 14 - (-16/2)^2
Simplifying the equation further:
y = (x^2 - 16x + 64) + 14 - 64
y = (x - 8)^2 - 50
Therefore, the vertex of the graph y = x^2 - 16x + 14 is (8, -50).