Question

Determine the equation of the graph shown, in factored form.

Answer 1

To solve the given problem we will use the fact that the number of times the graph cuts the axis, that will be the degree of the function.

Given data:

We can see from the graph we can see that y- intercept is

`(0,(9)/(4))`

and x- intercept are

`(-1,0)\text{ and (3,0)}`

Since the x - intercepts are

`(-1,0)\text{ and (3,0)}`

So, equation will have the form

`y=(x+1)(x-3)\ldots(1)`

But this equation does not satisfy the point

`(0,(9)/(4))`

As on substituting x=0 in equation 1 we get

`y=(0+1)(0-3)=-3`

So, we should multiply the equatiojn (1) with some constant to satisfy the given condition.

So, the equation will be

`y=(-9)/(12)(x+1)(x-3)\ldots(2)`

So, the required equation is

`y=(-3)/(4)(x+1)(x-3)`