Write an equation of the parabola in intercept form that passes through (0,-18) with x-intercepts of 9 and 1

Answer 1

Hi Candria,

Intercept form is the following:

y=a(x-p)(x-q)

where p and q are the x coordinates at which the parabola crosses the x-axis (that is, the x-intercepts).

Our job is to find the values of a, p and q.

In this case, p=9 and q=1 since you are told in the problem these are the x-intercepts.

Plugging in the values for q and p we get:

y=a(x-9)(x-1)

Now we just need to find the value of a

In the problem we are told that this parabola passes through x=0 and y=-18. So we plug in those values into our expression and solve for a:

-18=a(0-9)(0-1)

-18=a(-9)(-1)

-18=9a

a=-2

Finally, we plug in the value of a into our expression:

y=-2(x-9)(x-1)

Hope this helps.