SOLUTION: Sketch a parabola that has a turning point of (0, -6) and complex roots. What else can you infer about the parabola?

Algebra ->  Graphs -> SOLUTION: Sketch a parabola that has a turning point of (0, -6) and complex roots. What else can you infer about the parabola?       Log On


   

Question 118376: Sketch a parabola that has a turning point of (0, -6) and complex roots. What else can you infer about the parabola?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the parabola has complex roots, this means the parabola does not cross the x-axis. Also, the vertex of the parabola is (0,-6), so this means that the vertex is below the x-axis. Since the graph does not cross the x-axis, and the vertex is below the x-axis, the entire graph must be below the x-axis.

So the parabola might look like this (there are many ways to draw this. The important thing to remember is the turning point or vertex is at (0,-6) and it does not cross the x-axis):

graph%28500%2C500%2C-15%2C15%2C-15%2C15%2C-%28x-0%29%5E2-6%29


So we can see that the entire parabola is underneath the x-axis. Also we can see that the parabola is upside down.