Quadratic Function: Converting Graph to Algebraic Form at Point (-2)

Find the corresponding algebraic representation for the function

The problem involves determining the algebraic formula of a function represented by a graph of a parabola. From the axes on the graph, we observe that the graph intersects the y-axis at $y = -2$. This intersection indicates that the constant term $c$ in the quadratic function $y = x^2 + c$ is $-2$.

• Step 1: Start with the parabola formula $y = x^2 + c$. Since this is a standard vertical parabola centered on the y-axis (no $x$ term with a coefficient), it takes the form $y = ax^2 + c$.
• Step 2: From the graph, we see that when $x = 0$, $y = -2$. Substituting into the equation gives us: $y = 0^2 + c = -2$.
• Step 3: Solve for $c$. Here, it is evident that $c = -2$ since the equation simplifies directly to this when $x = 0$.

Therefore, the equation of the parabola is $y = x^2 - 2$, which corresponds to choice 3 in the provided options.

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