A parabola y=ax^2+bx+c has vertex (4,3). If (3,0) is on the parabola, find a.
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
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
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.
To find the value of 'a', we can use the information given about the vertex and a point on the parabola. The vertex form of a parabola is given by the equation:
y = a(x - h)^2 + k
Where (h, k) represents the vertex of the parabola. In this case, we are given that the vertex is (4, 3). So, we have:
y = a(x - 4)^2 + 3
We are also given that the point (3, 0) lies on the parabola. Substituting these values into the equation, we get:
0 = a(3 - 4)^2 + 3
Simplifying further:
0 = a(-1)^2 + 3
0 = a + 3
To find the value of 'a', we can subtract 3 from both sides of the equation:
a + 3 - 3 = 0 - 3
a = -3
Therefore, the value of 'a' is -3.