Question

Given the function f (x) on the graph and g(x) = x + 5, find where
f(x) = g(x).

Answer 1

Answer: (-4,1) (-1.4)

Explanation:

`f(x)=-(x+2)^2+5\\g(x)=x+5\\-(x+2)^2+5=x+5\\-(x^2+2*x*2+2^2)=x\\-(x^2+4x+4)=x\\`

Multiply both parts of the equation by -1:

`x^2+4x+4=-x\\x^2+4x+4+x=-x+x\\x^2+4x+x+4=0\\x*(x+4)+(x+4)=0\\(x+4)(x+1)=0\\x+4=0\\x=-4\\y=-4+5\\y=1\\Hence,\ (-4,1)\\x+1=0\\x=-1\\y=-1+5\\y=4\\Hence, \ (-1,4)`