Question

Determine the rule of a quadratic function in factored

form given the following information:
.
the zeros are (-2,0) and (4,0)
it passes through the point (5,14)
.

Answer 1

`y=2(x+2)(x-4)`

Explanation:

Hi there!

Factored form:
`y=a(x-r)(x-s)` where r and s are two zeros

Given that the zeros are (-2,0) and (4,0), we know that -2 and 4 are r and s in the above equation. Plug these in:

`y=a(x-(-2))(x-(4))\\y=a(x+2)(x-4)`

Now, to solve for a, plug in the given point (5,14) as (x,y):

`14=a(5+2)(5-4)\\14=a(7)(1)\\14=7a\\a=2`

Therefore, a=2. Plug this back into the original equation:

`y=2(x+2)(x-4)`

I hope this helps!