Answer:
The correct options are B and C.
Step-by-step explanation:
Graph A represents the parent quadratic function.
[tex]f(x)=x^2[/tex]
The vertex from of a parabola is
[tex]y=a(x-h)^2+k[/tex]
where, (h,k) is vertex and a is a constant.
If |a|>1, then parent function is stretched by factor a and If 0<|a|<1, then parent function is compressed by factor a.
The vertex of graph B is at (1,0). So the function of graph B is
[tex]g(x)=a(x-1)^2+0[/tex]
[tex]g(x)=a(x-1)^2[/tex]
Graph B passes through (3,0), so
[tex]3=a(0-1)^2[/tex]
[tex]3=a[/tex]
The value of a is 3. So, the function of graph B is
[tex]g(x)=3(x-1)^2[/tex]
If means the graph A stretched vertically by factor 3 and translate 1 unit to the right.
Therefore the correct options are B and C.
