Parabola question

Question

How do you know if a parabola opens up or down by looking at the equation?

Answer 1

Hello Edwin,

You look at the sign of the coefficient of x²:

1. if the coefficient is positive, the parabola opens up
2. if the coefficient is negative, the parabola opens down

Example: y = -3x² + 5x - 6

Here the coefficient of x² is -3; because -3 is negative, this parabola will open down

Likewise, the parabola y = x² -2x +3 will open up because the coefficient of x², 1, is positive.