Complete the square for the following quadratic equation to determine its solutions and the location of its extreme value
y = -x + 4x + 12
a
x=2 + 277
extreme value at (2.16)
b.
x = -2,6
extreme value at (2,12)
c.
x = -2.6
extreme value at (2.16)
d. x = 2 + 277
extreme value at (2,12)

Option C. x = -2,6  extreme value at (2.16)

Step-by-step explanation:

we have

This is the equation of a vertical parabola open down

The vertex is a maximum (extreme value)

Convert the equation into vertex form

Complete the square

Group terms that contain the same variable and move the constant term to the left side

Factor -1

Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

-----> equation of the parabola in vertex form

The vertex is the point (2,16) ----> is a maximum (extreme value)

Determine the solutions of the quadratic equation

For y=0

square root both sides

therefore

The solutions are x=-2 and x=6

The extreme value is (2,16)

the answer is b