I have a parabella with points (-3,0) and (5,0). These are two points are on the x-axis. The bottom point is (1,-4). what would the equation for this be in the form of y=a(x-r)(x-s)
(-3,0) and (5,0) are on your parabola i.e. if you plug in -3 and -5 into your equation, you'll get 0.
Now looking at your equation:
The only way that your equation will yield 0 is if either the red or blue is equal to 0 (remember, : either a or b or both are 0). Since we know x = -3 and 5 will work, we can see that r = -3 and s = 5 (since 3 - (-3) = 0 and 5 - 5 = 0).
Now all that's left to do is solve for a. You have the point (1, -4) - i.e. if x = 1 and you plug it into your equation, you'll get y = -4. So plug this into your expression from above and you'll get your parabola.
Set y = 0 and factor your expression.
For example, if your question was:
Find the x-intercepts of .
Set y = 0 and factor your expression:
Equate each bracketed term to 0 (like I mentioned earlier if then either a or b or both are equal to 0).
So, your x-intercepts are (-5, 0) and (-2, 0).
Now apply similar reasoning to your question.
There are many ways to factor trinomials with a coefficient other than 1 in front of the term.
I like doing it this way. For the general trinomial , we find two numbers such that they multiply to and add up to . Let's call these two numbers and . We split up bx into ux + vx and you should be able to factor it.
An example would probably help clear this up for you.
We have to find two numbers such that they multiply to and add up to 14. 9 and 5 should come up in your head.
So, we split up 14x into 9x and 5x:
Now factor each coloured expression as much as you can:
Notice the (x+3) in pink? Factor it out of the entire expression and you'll get your factored form:
Voila. See if you can apply this to your expression.