Question

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

Answer 1

Answer:

The point that represents the bottom of the pool is $(x,y) = (-4, -16)$.

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:

$y-k = C\cdot (x-h)^{2}$ (1)

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$h$, $k$ - Coordinates of the vertex, dimensionless.

$C$ - Constant, dimensionless.

The parabola is represented by $f(x) = x^{2}+8\cdot x$ and we proceed to transform into the desired form:

1) $f(x) = x^{2}+8\cdot x$ Given.

2) $f(x) = (x^{2}+8\cdot x + 16)-16$ Modulative property/Existence of the additive inverse.

3) $f(x) +16 = (x+4)^{2}$ Compatibility with the addition/Modulative property/Existence of the additive inverse/Perfect square trinomial.

4) $y + 16 = (x+4)^{2}$ Notation/Result.

Hence, the point that represents the bottom of the pool is $(x,y) = (-4, -16)$.