Question

Which equation represents a parabola that opens upward, has a minimum value of 3, and has an axis of symmetry at x= 3?

Answer 1

Answer:

$y=(x-3)^2+3$

Step-by-step explanation:

The correct question is

Which equation represents a parabola that opens upward, has a minimum value of y=3, and has an axis of symmetry at x= 3?

Verify each case

case 1) we have

$y=(x+3)^2-6$

This a vertical parabola open upward (the leading coefficient is positive)---> is ok

The vertex represent a minimum ---> is ok

The vertex is the point (-3,-6)

The minimum value of y=-6 ----> is not ok

The axis of symmetry is x=-3 ----> is not ok

case 2) we have

$y=(x+3)^2+3$

This a vertical parabola open upward (the leading coefficient is positive)---> is ok

The vertex represent a minimum ---> is ok

The vertex is the point (-3,3)

The minimum value of y=3 ----> is ok

The axis of symmetry is x=-3 ----> is not ok

case 3) we have

$y=(x-3)^2-6$

This a vertical parabola open upward (the leading coefficient is positive)---> is ok

The vertex represent a minimum ---> is ok

The vertex is the point (3,-6)

The minimum value of y=-6 ----> is not ok

The axis of symmetry is x=3 ----> is ok

case 4) we have

$y=(x-3)^2+3$

This a vertical parabola open upward (the leading coefficient is positive)---> is ok

The vertex represent a minimum ---> is ok

The vertex is the point (3,3)

The minimum value of y=3 ----> is ok

The axis of symmetry is x=3 ----> is ok