SOLUTION: If your equation is -0.2x + x² + 0.2 = 0, does this parabola open up or down? Which term's coefficient determines that?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: If your equation is -0.2x + x² + 0.2 = 0, does this parabola open up or down? Which term's coefficient determines that?       Log On


   

Question 475472: If your equation is -0.2x + x² + 0.2 = 0, does this parabola open up or down? Which term's coefficient determines that?

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Skip the " = 0" part, since the graph would be two points instead of a parabola.

The function f(x) = -0.2x + x^2 + 0.2 goes to positive infinity on both sides, so the parabola opens down. The x^2 coefficient determines this because it has the highest degree.

(I actually never learned a parabola "opening up" or "opening down" in school, it is a vague definition and hardly anyone uses that definition in higher-level mathematics.)