Answer:
The constant term in the function is 5
Step-by-step explanation:
we have
[tex]f(x)=x^{2}+8x+b[/tex]
where
b is the y-intercept or the constant term of the function
Remember that
The x-intercept is the value of x when the value of the function is equal to zero
so
For x=-3 ----> f(x)=0
For x=-5 ----> f(x)=0
substitute any of the intercepts in the function
For x=-3
[tex]0=(-3)^{2}+8(-3)+b[/tex]
[tex]0=9-24+b[/tex]
[tex]0=-15+b[/tex]
[tex]b=15[/tex]
[tex]f(x)=x^{2}+8x+15[/tex]
Verify with the other intercept
For x=-5
[tex]0=(-5)^{2}+8(-5)+15[/tex]
[tex]0=25-40+15[/tex]
[tex]0=0[/tex] ---> is true
therefore
The constant term in the function is 5
