Complete the square to determine the minimum or maximum value of the function defined by the expression.

−x² + 10x + 5

a. maximum value at 30
b. minimum value at 30
c. maximum value at −30
d. minimum value at −30

provide a full explanation, you!

A. maximum value at 30

Step-by-step explanation:

−x² + 10x + 5

First, factor out the leading coefficient from the first two terms:

-1 (x² − 10x) + 5

Take half of the next coefficient, square it, then add and subtract the result.

(-10/2)² = 25

-1 (x² − 10x + 25 − 25) + 5

-1 (x² − 10x + 25) + 25 + 5

-1 (x² − 10x + 25) + 30

Factor the perfect square.

-1 (x − 5)² + 30

The equation is now in vertex form.  This is a downwards parabola with a vertex at (5, 30).  Since the parabola points down, the vertex is a maximum.

Step-by-step explanation:

SLOPE FORMULA:

y₂-y₁/x₂-x₁=rise/run

SLOPE-INTERCEPT FORM:

y=mx+b

m represents the slope.

b represents the y-intercept.

y₂=(-16)

y₁=47

x₂=2

y₁=(-4)

Solve.

Furthermore, the y-intercept is 5.

y=-21/2x+5

The correct answer is y=-21/2x+5.