Question

How do I solve this:

Find the equation of a parabola that has x-intercepts -3 and 1 and a y-intercept of 6.

Answer 1

y=a(x-r)(x-s)

I get how to solve but don't get this step

6 = a (0+3)(0-1)

Where do the "0"s come from in the equation?

Answer 2

The x-intercept is the point at which y = 0 (that means the point that lies on the x axis). Likewise, the y-intercept is the point at which x = 0 (the point that lies on the x axis).

So the 0 is there because one variable was set to 0.

Answer 3

So in the equation y = a(x-r)(x-s)

the x's are 0 in this case because we are given a y intercept right?

But if say y way 6, 1 then in the equation the x's would have both been 1 right?

Answer 4

You substitute only one variable at a time. So

y = a(0-r)(0-s)

or

0 = a(x-r)(x-s)

Answer 5

yea but if the questions said that y was 6,1 then both x's would have been 1 and the y would have been 6 right?

Answer 6

Yes, that is correct.

Answer 7

Thanks o_o