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

$(0,\frac{9}{4})$

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

$(0,\frac{9}{4})$

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

$y=\frac{-9}{12}(x+1)(x-3)\ldots(2)$

So, the required equation is

$y=\frac{-3}{4}(x+1)(x-3)$