Maths: Polynomial Graphs and Values?
Let f be a quartic polynomial (ie. a polynomial of degree 4). Suppose that f has zeros at -2; 1; 3; 4 and that f (0) = 4.
- Sketch a graph of f.
- If f(x) is written in the form:
f (x) = A(x - a)(x - b)(x - c)(x - d)
then find the values of A; a; b; c; d.
- gAytheistLv 67 years agoFavorite Answer
Well the curve has to go through the x axis at each of the zeros. Now, from -2 to 1 it must go UP to 4 at x = 0. This means the curve must be going negative (pointing downwards) as you go from -2 to larger negative numbers (i.e. smaller numbers). That means the overall coefficient A in front of the equation must be negative.
To solve for the value of A:
A(x+2)(x-1)(x-3)(x-4) = 4 when x = 0
A(2)(-1)(-3)(-4) = 4
-24A = 4
A = - 1/6
- 7 years ago