Question

For the following exercises, use the graphs to write the formula for a polynomial function of least degree.

Answer 1

According to this topic, we know it is a polynomial with 3 degrees, and it has three zeros which are

`x=-2,-2,3`

and it passes through (0,-3).

Therefore, we suppose its equation is:

`f(x)=a(x+2)(x+2)(x-3)=a(x+2)^2(x-3)`

Then (0,-3) is located in f(x).

Hence, let us solve for the value of 'a' if the y-intercept is (0,-3).

`\begin{gathered} \text{when, x = 0, y = -3} \\ f(0)=-3 \\ \therefore-3=a(0+2)(0+2)(0-3) \\ -3=a(2)(2)(-3)=-12a \\ -3=-12a \\ a=(-3)/(-12)=(1)/(4) \\ \therefore a=(1)/(4) \end{gathered}`

Therefore, the formula for the polynomial function of least degree is

`f(x)=(1)/(4)(x+2)^2(x-3)`