Write in standard form the equation of the parabola with ver

Write, in standard form, the equation of the parabola with vertex (-1, 5) whose graph passes through the point (1, 2). Standard form: y = a(x- h)^2 + k

Solution

Standard form of equation for a parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
For given problem:
Using coordinates of given vertex at (-1,5)
y=A(x+1)^2+5
Using coordinates of given point (1,2)

2=A(1+1)^2+5

2=4A+5
4A=-3
A=-3/4
Equation of parabola:
y=(-3/4)(x+1)^2 + 5