Question

A parabola y=ax^2+bx+c has vertex (4,3). If (3,0) is on the parabola, find a.

Answer 1

from the vertex, you know that
y = a(x-4)^2 = a(x^2-8x+16)+3
Since y(3)=0,
a(3-4)^2+3 = 0, so a = -1

Answer 2

mmmhhh,

you know the equation must be
y = a(x - 4)^2 + 3
but (3,0) lies on it, so
0 = a(3-4)^2 + 3
0 = a + 3
a = -3

Answer 3

Oh, yeah -- that's what I meant
Funny how things like that slip past...
I must have been thinking of the (-1)^2 and being careful about the sign, and not the value.
Thanks for the catch.