SOLUTION: Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether it's vertex lies above, on or below the x-axis. Y=4x^2-1

Algebra ->  Graphs -> SOLUTION: Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether it's vertex lies above, on or below the x-axis. Y=4x^2-1      Log On


   

Question 889807: Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether it's vertex lies above, on or below the x-axis. Y=4x^2-12x+12
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
If y=0 then 4x%5E2-12x%2B12=0
x%5E2-3x%2B3=0
zeros are x=%283%2B-+sqrt%289-12%29%29%2F2
x=%283%2B-+sqrt%28-3%29%29%2F2 NOT a real number.

The parabola does not share any points with the x-axis. The vertex is a minimum as found that the coefficient on x%5E2, 4, is positive; and the vertex is above the x-axis.