Question

Write an equation of a polynomial with the given characteristics: a quadratic function has x -intercepts of -3 and 1, and a y-intercept of (0,9).

Answer 1

f(x) = -3x^2 - 6x + 9.

Explanation:

As the x intercepts are - 3 and 1 we can write it as:

f(x) = a(x - 1)(x + 3) where a is a constant to be found.

As the - intercept is at (0, 9), x =0 when f(x) = 9 so we can also write:

a( 0 - 1)(0 + 3) = 9

(-1)(3)a = 9

a = 9 / -3

= -3.

So the equation is f(x) = -3(x - 1)(x + 3)

In expanded form it is

-3(x^2 + 2x - 3)

= -3x^2 - 6x + 9.

Answer 2

f(x) = -3(x+3)(x-1)

Explanation:

x = -3 & 1; f(x) = 9

f(x) = a(x-r1)(x-r2)

f(0) = a(x-r1)(x-r2) = 9; 9 = a(0-(-3))(0-1)

9 = a(3)(-1); 9 = a(-3)

a = -3

f(x) = -3(x+3)(x-1)