For what values of a the graph of the function y = ax ^ 2 passes through the point A (-3 27).

As is known, if the graph of the function y = f (x) passes through the point M (x0; y0), then the condition y0 = f (x0) must be satisfied.
For our example, the function is y = a * x ^ 2. In addition, point A, through which the graph of the function y = a * x ^ 2 passes, is specified by coordinates A (–3; 27).
Let’s compose the equality 27 = a * (–3) ^ 2. Considering this equality as an equation for the parameter a, we solve it. So, 9 * a = 27. We have a = 27: 9 = 3. Therefore, for a = 3, the graph of the function y = a * x ^ 2 passes through the point A (–3; 27).
Answer: a = 3.