SOLUTION: 9.) 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

Algebra ->  Test -> SOLUTION: 9.) 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       Log On


   

Question 195118: 9.) 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 = 2x2 + x + 3







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 = 3x2 - 12x + 12

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
9)y=2%28x%5E2%2B1%2F2x%29%2B3
:
y=2%28x%5E2%2B1%2F2x%2B1%2F16%29-1%2F8%2B3
:
y=2%28x%2B1%2F4%29%5E2%2B23%2F8
:
equation with the form y=ax%5E2open up or down....if a postive it opens up and if a is negative opens down
:
since the vertex is at (-1/4,23,8) and lies above the x axis and a is positive meaning this parabola opens up then we know it doesnt cross the x axis.
:
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x%5E2%2Bx%2B3%29
:
10) y=3%28x%5E2-4x%2B4%29-12%2B12
:
y=3%28x-2%29%5E2
:
since the vertex is at (2,0) and lies on x axis and a is positive meaning this parabola opens up then we know has only one point in common with the x axis and that point is (2,0)
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x%5E2-12x%2B12%29