Question

Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis.

y = 3x^2 - 12x + 12

Answer 1

solve for x = 0 and you will find your answer

Answer 2

factor as y = 3(x-2)^2
From this we see that y is always positive and touches the x-axis once at x=2

Answer 3

so would the answer be 1 point in common; vertex on x-axis