Whoever gets right gets
complete the square to determine the maximum or minimum value of the function defined by the expression. x2 − 2x − 5

a. minimum value at 1

b. minimum value at -6

c. minimum value at -1

d. maximum value at −6

Answer B:  min. value at -6

Step-by-step explanation:

Complete the square of f(x) = x^2 - 2x - 5.

Note:  Please use " ^ " to denote exponentiation, as shown.

Start with f(x) = x^2 - 2x - 5.

Identify the coefficient of the x term:  it is 2.

Take half of that and square your result:  (1/2)(2) = 1, and then 1^2 = 1.

Add and subtract this 1 between the 2x term and the constant term:

f(x) = x^2 - 2x    + 1   - 1  - 5

Rewrite x^2 - 2x + 1 as a perfect square:

f(x) = (x - 1)^2 - 1 - 5, or    f(x) = (x - 1)^2 - 6

Compare this to the standard form

                                        f(x) = (x - h)^2 + k

We see that h = 1 and k = -6.

The vertex is located at (h, k); here, it's located at (1, -6).

Thus, the minimum value of this function is at the vertex (1, -6).

This agrees with Answer B:  min. value at -6.

Equation of parabola is y = x² - 5 .

Step-by-step explanation:

Given  : parabola with a vertex at (0, -5).

To find :  which of the following equations is of a parabola.

Solution : We have given  vertex at (0, -5).

Vertex form of parabola   y = a(x - h)² + k .

Where (h ,k ) is vertex

We have h = 0 , k = -5 .

Equation : y = 1(x - 0)² - 5

y = x² - 5 .

Therefore, Equation of parabola is y = x² - 5 .