How do you determine the equation of a parabola which has a vertex of (-1,3) and passes through the point (0,5)?

Answer 1

The equation of a parabola is f(x) = + or - a (x-h)^2 + h with h, k being the vertex. Put the vertex and point in and solve for a: 5 = a (0-(-1))^2 + 3. Simplifying: 5 = a(1)^2 + 3; 5 = a + 3; a = 2. Thus the equation is the following: f(x) = 2(x+1)^2 + 3. Notice that the substitution of the vertex in makes the x part the opposite sign and the last term part the same sign.

Answer 2

First of all, the equation you need is Ax²+Bx+C and immediately you know that C=5.

Then

A-B+5=3 <--- the equation passes through (-1,3)

and -2A+B=0 <----- the slope at the vertex=0