Convert Quadratic Graph to Algebraic Function: Point (-6) Analysis

Find the corresponding algebraic representation for the function

To solve this problem, we will determine the vertical shift given to the parent function $y = x^2$ to form the observed parabola.

• Identify that the problem involves a vertical translation of the parabola $y = x^2$.

• The function takes the form $y = x^2 + c$, where $c$ indicates the vertical shift.

• From the graph given, it is seen that the vertex of the parabola is situated at $y = -6$ when viewed from the intersection with the y-axis.

• This downward shift corresponds to the constant $c$ being negative, specifically $c = -6$.

• By this observation, the function becomes $y = x^2 - 6$.

Therefore, the solution to the problem is $y = x^2 - 6$, matching choice 2.