How do I write a quadratic function whose zeroes are -3 and 5?

Question

Hi, I am struggling on this question. I was taught a way that is not like this problem, please help.

Answer 1

Think of it this way: normally you start out with a quadratic and work to factor out to get TO the -3 and 5. Now you're starting at the other end.

0 = (x + 3)(x - 5)

If you notice the signs, they're the invers of the numbers. That's because we need that 3 to cancel the x = -3, and the same for the -5 cancelling the x = 5.

From here, we distribute, or FOIL (First Outer Inner Last):

x * x = x²

x * -5 = -5x

3 * x = 3x

3 * -5 = -15

 

That leads us to have so far x² - 5x + 3x - 15

Simplify that by combining like terms, and you'll have yourself a pretty little quadratic.