Question

Hello! I need some help with this homework question, please? The question is posted in the image below. Q7

Answer 1

Since -3 is a zero of the function then x=-3

This implies

x+3 is a factor of the polynomial

Following the same procedure, since 2 and 5 are zeros then

x-2 and x-5 are factors

Hence the polynomial can be written as

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

Since the graph passes through the point (7,300)

Substitute x=7 and y=300 into the equation

This gives

`300=a(7+3)(7-2)(7-5)`

Solve the equation for a

`\begin{gathered} 300=a(10)(5)(2) \\ 300=100a \\ a=(300)/(100) \\ a=3 \end{gathered}`

Substitute a into the equation of the polynomial

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

Therefore the answer is

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