Question

Can someone help me please

10. 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

From my thinking, what we can do first is factorise x^2-12x+12 (either using solver on the graphics calculator or using the quadratic formula)
I got x=10.89 and x=1.10 as my two x intercepts.
Therefore, I know it will pass through two points on the x axis and since it is a positive parabola, the vertex will be below the x axis.

.. i hope this helps!