Question

Write the equation of the parabola that has a vertex (1, -1) and passes through the point (2,5

Answer 1

the equation of a parabola is:

y = a(x-h)² + k

where (h,k) is the vertex.

since you are given (h,k) and (x,y), you can find "a" by plugging in the know values and solving:

5 = a(2-1)² - 1
5 = a -1
a = 6
a = -5/4

quadratic function:

y = f(x) = (6)(x - 1)² -1
6(x^2-2x+1)-1
y=6x^2-12x+5