Question

Given the function ƒ(x) = x 2 - 4x - 5

Identify the zeros using factorization.
Draw a graph of the function. Its vertex is at (2, -9).

Answer 1

Zeros of the given function are x=5 and x=-1.

Explanation:

f(x)=x^2-4x-5

f(x)=x^2+1x-5x-5

f(x)=x(x+1)-5(x+1)

f(x)=(x-5)(x+1)

To find zeros, we need to set f(x)=0

0=(x-5)(x+1)

0=(x-5) or 0=(x+1)

0=x-5 or 0=x+1

5=x or -1=x

Hence zeros of the given function are x=5 and x=-1.

We can plug some random numbers like x=0,1,2,... into given function to find few points then graph those points and join them by a curved line.

That will give the final graph as attached below:

for x=0,

f(x)=x^2-4x-5

f(0)=0^2-4(0)-5

f(0)=0-0-5

f(0)=-5

Hence first point is (0,-5)

Similarly we can find more points.