The shape of an underground pool follows a parabola with the function LaTeX: f\left(x\right)=x^2+8xf ( x ) = x 2 + 8 x. What point represents the bottom of the pool? Group of answer choices

The point that represents the bottom of the pool is .

Step-by-step explanation:

Given that the shape of the underground pool is a parabola, that is, a second order polynomial. Then, the point that represents the bottom of the pool is the vertex, which is contained in the standard form of the parabola. That is:

(1)

Where:

- Independent variable, dimensionless.

- Dependent variable, dimensionless.

, - Coordinates of the vertex, dimensionless.

- Constant, dimensionless.

The parabola is represented by and we proceed to transform into the desired form:

1) Given.

2) Modulative property/Existence of the additive inverse.

3) Compatibility with the addition/Modulative property/Existence of the additive inverse/Perfect square trinomial.

4) Notation/Result.

Hence, the point that represents the bottom of the pool is .