Answer: -7.2
Step-by-step explanation:
The vertex form of quadratic equation :[tex]f (x) = m(x - a)^2 + b,[/tex] where (a,b) is the vertex.
Given: The quadratic function g(x) has a vertex at (-5, 0).
Put (a,b)= (-5,0) for function g(x), we get
[tex]g(x)=m(x-(-5))^2+0\\\\\Rightarrow\ g(x)=m(x+5)^2[/tex]
Also, its y-intercept is (0, -5).
Put x= 0 and g(x) =-5
[tex]-5=m(0+5)^2\\\\\Rightarrow\ -5=m(25)\\\\\Rightarrow\ m=\dfrac{-5}{25}\\\\\Rightarrow\ m=\dfrac{-1}{5}[/tex]
so, [tex]g(x)=-\dfrac{1}{5}(x+5)^2[/tex]
For g(1), put x=1
[tex]g(1)=-\dfrac{1}{5}(1+5)^2\\\\=-\dfrac{1}{5}(6)^2=-\dfrac{1}{5}(36)\\\\=-7.2[/tex]
Hence, g(1) is -7.2.
