Question

Which graph shows the quadratic function y = 3x2 − 12x + 10? (5 points)

Answer 1

The graph in option D.

Step-by-step explanation

The given function is:

`y = 3 {x}^(2) - 12x + 10`

We complete the square to obtain:

`y = 3( {x}^(2) - 4x) + 10`

`y = 3( {x}^(2) - 4x + {( - 2)}^(2) ) + 10 - 3 {( - 2)}^(2)`

`y = 3{( x- 2)}^(2)+ 10 - 12`

`y = 3{( x- 2)}^(2) - 2`

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.