Write a quadratic function f whose zeros are -5 and -4.

Answer 1

A function f(x) having zeros at certain locations mean that, when x is one of the "zero" values, f(x) evaluates to zero. f(x) is a quadratic function, so it will generally be written f(x) = ax^2+bx+c, but it can also be written as f(x) = d*(x-z1)(x-z2).

For example, in our case we want f(x) to be zero when x is -5. This is true of the expression (x+5), so if we multiply our function that we're building by x+5 it will have a zero at -5

Similarly, we need a (x+4) term to set a zero at -4.

f(x) = (x+5)(x+4)

Then we multiply out the expressions:

f(x) = x^2 + 9x + 20

Answer 2

If a zero is -5, that means the factor associated with that zero is (x + 5)

If a zero is -4, that means the factor associated with that zero is (x + 4)

So, a quadratic function with zeros of -5 and -4 COULD be:

f(x) = (x + 5)(x + 4) or (multiplying it out):

f(x) = x² + 9x + 20

I say "COULD" be, because it's possible to put a multiplier in front of the two factors like this:

f(x) = 2(x + 5)(x + 4) or

f(x) = 3(x + 5)(x + 4)

and still have zeros of -5 and -4 (so there is more than one answer)

Answer 3

x=-5

x+5=0

x=-4

x+4=0

multiply those two factors together

(x+5)(x+4)

f(x) = x^2 + 9x +20

Answer 4

f(x) = (x + 5)(x + 4)