Writé the equation for a parabola with x-intercepts of 1 and -3 and passes through
(-9,28).

Step-by-step explanation:

Equation of the Parabola

The general form of the equation of the parabola is:

We can try to find the values of a,b, and c by using the three given points (1,0),(-3,0),(-9,28).

However, we'll use an easier method. There is another form of the parabola in case we know its roots, also called zeros or x-intercepts. If p and q are the roots of f, then f can be expressed as:

We already know the values of p=1 and q=-3, thus replacing them into the equation, we have:

We only need to find the value of a. We do that by using the point (-9,28):

Operating:

Solving for a:

Thus, the equation of the parabola is: