SOLUTION: Please let me know why does the parabolic equation {{{y=X^2}}} has two roots though the parabola touches the x-axis only once.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Please let me know why does the parabolic equation {{{y=X^2}}} has two roots though the parabola touches the x-axis only once.      Log On


   



Question 774692: Please let me know why does the parabolic equation y=X%5E2 has two roots though the parabola touches the x-axis only once.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

y=X%5E2..... the basic upward opening parabola
since you have x%5E2, always will be two x have the same y value
example:
if x=1 => y=%281%29%5E2=> y=1
if x=-1 => y=%28-1%29%5E2=> y=1
or
if x=2 => y=%282%29%5E2=> y=4
if x=-2 => y=%28-2%29%5E2=> y=4
it happens to be x=0 first, and 0 is neither positive nor negative, so the lowest point of this parabola is the vertex which is at (0,0)
and parabola touches x-axis%2C+as+%7B%7B%7By-axis as well, only ones

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%29+