Question

y=x^2-8x+6 complete the square to determine the vertex and maximum or minimum value. Determine the number of x-intercepts.

Answer 1

Below in bold.

Explanation:

y = x^2-8x+6

y = (x - 4)^2 - 16 + 6

y = (x - 4)^2 - 10

So the vertex is at (4, -10)

The coefficient of x^2 of this function is 1 ( positive) so there will be a minimum value.

Minimum value = -10.

x-intercepts:

(x - 4)^2 - 10 = 0

(x - 4)^2 = 10

x - 4 = +/- √10

x = 4 +/- √10

- therefore there are 2 x-intercepts.