Question

Under what conditions, the graph of quadratic polynomial $p\left(x\right)=a{x}^2+bx+c$ is an upward parabola or a downward parabola

Answer 1

Condition for the graph of quadratic polynomial $p\left(x\right)=a{x}^2+bx+c$ is an upward parabola or a downward parabola:

If the coefficient of $x^2$ is positive then it is an upward parabola.

If the coefficient of $x^2$ is negative then it is a downward parabola.

Hence, $a>0$ then it is an upward parabola and $a<0$ then it is a downward parabola.