Final answer:
To find the equation of a parabola with vertex (-2, 5), use the vertex form y = a(x - h)^2 + k, substitute the vertex into the equation, use a given point to solve for 'a', then write the complete parabolic equation.
Step-by-step explanation:
To determine the equation of a parabola with vertex (-2, 5) that goes through a given point, we need to use the vertex form of a parabolic equation, which is:
y = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola. In this case, h = -2 and k = 5, so our equation starts as:
y = a(x + 2)^2 + 5
To find the value of 'a', we need to use the given point that lies on the parabola. Assuming the coordinates of this point are (x1, y1), we would substitute these values into the equation and solve for 'a'. Once 'a' is found, the full equation of the parabola would be:
y = a(x + 2)^2 + 5.