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 = x2 – 12x + 12


1 point in common; vertex on x-axis
2 points in common; vertex below x-axis
2 points in common; vertex above x-axis
no points in common; vertex above x-axis

Answer 1

y = x2 – 12x + 12

Answer 2

well the vertexes are (6,-24)

Answer 3

@Nylyak
do you know how to 'complete the square'?

Answer 4

just just the discriminant... if

\[b^2 - 4ac < 0\]

then the curve is positive definite... and won't cut the x axis

\[b^2 - 4ac = 0\]

has 1 point of contact with the x axis

\[b^2 - 4ac > 0\]

has 2 points of contact