SOLUTION: 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 = 2

Question 617716: 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

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your equation is:
y = 2x^2 + x - 3
set the equation equal to 0 and factor it.
the equation becomes:
2x^2 + x - 3 = 0
the factors of this equation are:
(2x + 3) * (x - 1) = 0
the roos of this equation are:
x = -3/2 and x = 1
those are the intersection of the graph of the equation with the x-axis.
the vertex of the equation must lie below the x-axis.
to confirm that, use the formula for the line of symmetry to find the vertex.
the standard form of a quadratic equation is equal to:
ax^2 + bx + c = 0
in your equation, that makes:
a = 2
b = 1
c = -3
the formula for the line of symmetry, which is also the x value of the vertex, is:
x = -b/2a
that becomes -1/4.
when x is equal to -1/4, y is equal to 2*(-1/4)^2 + (-1/4) - 3 which becomes:
1/8 - 1/4 - 3 which is equal to -3.125
that makes the vertex equal to (-1/4, -3.125)
the graph of this equation looks like this:

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