Question

What is the minimum value for g(x)=x^2-10x+16? Enter your answer in the box.

Answer 1

Answer:

- 9

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

add/subtract (half the coefficient of the x- term)² to x² - 10x

g(x) = x² - 10x + (- 5)² - (- 5)² + 16

      = x² - 10x + 25 - 25 + 16

     = (x - 5)² - 9 ← in vertex form

vertex = (5, - 9), hence

minimum value = - 9