Expert: Sherman D. - 5/1/2004

Question
1. Write the equation of any parabola that (a)opens up (b) is narrower than the identity and ©) has a vertex(-4,1).

Answer
Vertex Formula
x = -b/2a
-4 = -b/2a
-b = -8a
b = 8a

y = ax^2 + bx + c
1 = a(-4)^2 + 8a(-4) + c
1 = 16a - 32a + c
1 = -16a + c

-c = -16a - 1
c = 16a + 1

a > 0, because the parabola opens upward.

Here are some (a,b,c)s

(1,8,17),(2,16,33),(3,24,49),(4,32,65),(5,40,81), etc...


y = x^2 + 8x + 17
y = 2x^2 + 16x + 33
y = 3x^2 + 24x + 49
y = 4x^2 + 32x + 65
y = 5x^2 + 40x + 81

if you would like to try it for yourself, go to www.calculator.com, click on Graphing, and only type in the equation after the y = part. Do that, and you will get each one to have a vertex at (-4,1)