Question

Which of the following input-output tables represents the function graphed below?

Answer 1

Answer:

The function that represents the graph is $y = -2 + \frac{1}{2}\cdot x^{2}$.

Step-by-step explanation:

The graphic represents a vertical parabola, whose standard equation is:

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

Where:

$x$ - Independent variable, dimensionless.

$y$ - Depedent variable, dimensionless.

$h$ - Horizontal component of the vertex, dimensionless.

$k$ - Vertical component of the vertex, dimensionless.

$C$ - Vertex constant, dimensionless. Where $C > 0$ when vertex is an absolute minimum, otherwise it is an absolute maximum.

According to the figure, vertex is located in $(0, -2)$. Now we determine the vertex constant by using the following values in the standard equation:

$x = -2$, $y = 0$, $h = 0$, $k = -2$

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

$C = \frac{0-(-2)}{(-2-0)^{2}}$

$C = \frac{2}{4}$

$C = \frac{1}{2}$

The function that represents the graph is $y = -2 + \frac{1}{2}\cdot x^{2}$.