Write the cubic polynomial function f(x) in expanded form with zeros -5, -3, and 2, given that f(0) = -60.

Hi there!

Since we are given the zeros, we can derive the basic equation in expanded form:

x = -5

(x + 5)

x = -3

(x + 3)

x = 2

(x - 2)

y = (x + 5)(x + 3)(x - 2)

Multiplying the numbers, however, only gets -30. The y-intercept is -60, so we need a coefficent of 2 in the equation:

y = 2(x + 5)(x + 3)(x - 2)

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.