Question

Give an example of a quadratic equation and determine if it opens up or down and find the vertex

Answer 1

Let the qudratic equation be ax²+bx+c = 0

We know that the quadratic equation is parabola, so, every parabola depends on the leading co-effiecient(co-efficent of x² which decides the overall behaviour of polynomial because of its square power), it may open up or down.

if a<0, the equation sees like, -ax²+bx+c = 0

as x² term is always positive, with negative co-efficient, the parabola will be inverted always. i. opens down

if a>0, the equation sees like, +ax²+bx+c = 0

as x² term is always positive, with positive co-efficient, the parabola will be up always. i. opens up

Hope it helps!