Answer:
f(x)=
-Garph II
f(x)=
-Graph I
f(x)=
-Graph III
Explanation:
We are given that
f(x)=
![-x^2+2x-3](https://img.qammunity.org/2020/formulas/mathematics/high-school/pwk6x1yrb0w91lyx7uza226cfnrtnfonrl.png)
If substitute x=0 then we get f(0)=-3
It means y- intercept =-3
In given graph , there is no y- intercept=-3
It is false.
f(x)=
![-x^2-2x+3](https://img.qammunity.org/2020/formulas/mathematics/high-school/3s1u8kbuayfc778nkal2ctcijtfgpgqi2p.png)
If substitute x=0 the we get
f(0)=3
In second graph y - intercept =3
Substitute x=-1 then we get
f(-1)=-1+2+3=4
Hence, the function match with second graph.
f(x)=
![x^2-4x+5](https://img.qammunity.org/2020/formulas/mathematics/high-school/te1x0m54bxsbo6sk2rrzkcj64li34xrw9g.png)
If x=0 then we get
y- intercept =5
If we substitute x=2 then we get
f(1)=4-8+5=1
Hence, function match with First graph.
In third graph
Y- intercept =5
The vertices of parabola is (3,-4)
f(x)=
![x^2-6x+5](https://img.qammunity.org/2020/formulas/mathematics/high-school/klgww2l9r8b9co07pcvnh3ji11ykzd53a7.png)
If substitute x=0 then we get
y intercept =5
If we substitute x=3
Then we get
f(3)=
![3^2-6(3)+5](https://img.qammunity.org/2020/formulas/mathematics/high-school/u4arrj7n886gzia35p2ol57eg3cs1wdike.png)
f(3)=9-18+5=-4
Hence, the function match with third graph.