Question

How do I determine the zeros of the quadratic? y= -5(x-2)(x-7)

Answer 1

`x= 2 or 7`

Explanation:

The zeroes of a quadratic (or any function) is when `y=0`

To solve this, we take advantage of the zero factor theorem. Basically what it says that if I two things that multiply to zero, one of them must be zero. What this looks like is that if `ab=0`, then `a=0` or `b=0`. This works for any number of number of letters.

We are given that `y=-5(x-2)(x-7)`, so this is just:
`y=-5*(x-2)*(x-7)`, therefore either:
`-5=0`, but this is clearly not possible
`x-2=0`, which tells us x = 2 works
`x-7=0`, which tells us x = 7 works

Thus, we are left with the zeroes `x= 2 or 7`