SOLUTION: 1. You are given the coordinates of the vertex (2,-2) and of a point (-9,3) on a parabola. Find the coefficients for the equation of the parabola. Put in y=ax^2+bx+c form.

Question 616915: 1. You are given the coordinates of the vertex (2,-2) and of a point (-9,3) on a parabola. Find the coefficients for the equation of the parabola.
Put in y=ax^2+bx+c form.
2.Given the functions
f(x) = 5x2 − 4x + 2
g(x) = 3x + 6
Compute the following (you must simplify each polynomial as far as possible to receive full credit) Use the ^ (shift-6 on the keyboard) to enter a power. So to enter x2 + 3x + 1, you would type x^2 + 3x + 1.
What is f(g(x))?
What is g(f(x))?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
1. in vertex form ___ y = a(x - 2)^2 - 2
___ substituting the given point (to find a) ___ 3 = a(-9 - 2)^2 - 2 ___ 5 = 121a ___ a = 5/121
___ y = (5/121)(x - 2)^2 - 2 ___ y = (5/121)x^2 - (20/121)x - 238/121

2. f(g(x)) = 5(3x+6)^2 - 4(3x+6) + 2 = 45x^2 + 180x + 180 - 12x - 24 + 2 = 45x^2 + 168x + 158

g(f(x)) = 3(5x^2 - 4x + 2) + 6 = 15x^2 - 12x + 6 + 6 = 15x^2 - 12x + 12
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