Question

find the zeros of each functin
y=(x-2)(x+4)

Answer 1

The zeroes are always what makes the function equal to zero.

Answer 2

Set y = 0 and solve for x.

Answer 3

And in a product, any value that makes one of the product terms = 0 is a zero.

\[0 = (x-2)(x+4)\]That's true if \((x-2) = 0\) or if \((x+4) = 0\)

Answer 4

You can use this in reverse to construct a function that has the desired zeros.

If you want a function that has zeros of 3 and -7,
\[f(x) = a(x-3)(x-(-7)) = a(x-3)(x+7)\]There's your function! The value of \(a\) can be 1, or you can choose a different value if you need to have the function have a specific value at a given point.

In the following graph, all of the parabolas have the same zeros (aka roots), but a different value for \(a\).