Chapter 12, Problem 5CCSR

To determine

To find: the best equation which represents the graph.

Answer to Problem 5CCSR

The equation is ${\text{y=x}}^2-2$ .

Explanation of Solution

Given:

  

Concept used:

the graph of parabola had vertex either the vertex is Minima or Maxima.

If the curve is open upward then the point or vertex is Minima.

If the curve is open downward then the point or vertex is Maxima.

The equation of parabola which intersect x-axis and y-axis at origin is:

  ${\text{y=x}}^2$ .

Calculation:

The graph is vertical translation $2$ unit downward of the parent function ${\text{y=x}}^2$ .

Or

Since, the graph of the function is curve open upward therefore, there will be a Minima from the graph the minima point can be calculated as:

The $\text{y-}$ intercept is at $\left(0,-2\right)$ or the point of minima is at $\text{x=}0\text{,y=}-2$ .

Hence, the equation is ${\text{y=x}}^2-2$ .