ANSWER
The graph in option D.
EXPLANATION
The given function is:
[tex]y = 3 {x}^{2} - 12x + 10[/tex]
We complete the square to obtain:
[tex]y = 3( {x}^{2} - 4x) + 10[/tex]
[tex]y = 3( {x}^{2} - 4x + {( - 2)}^{2} ) + 10 - 3 {( - 2)}^{2}[/tex]
[tex]y = 3{( x- 2)}^{2}+ 10 - 12[/tex]
[tex]y = 3{( x- 2)}^{2} - 2[/tex]
The graph of this function opens upwards and has its vertex at (2,-2).
The y-intercept is 10.
From the options the graph that satisfies all these properties is D.
