When graphed, which parabola opens downward?
a. y = –3x2
b. y = (x – 3)2
c. y= 1/3x2
d. y = x2 – 3

Keywords:

quadratic function, quadratic term, positive coefficient, negative coefficient, parabola

For this case we have a quadratic function of the form , where . By definition, if the coefficient that accompanies the quadratic term of the equation is negative, the parabola open down. On the other hand, if the coefficient that accompanies the quadratic term of the equation is positive, the parabola opens upwards.

That said, we fear that is a function with the coefficient of the negative quadratic term, and therefore the parabola opens downwards.

Option A

there are infinitely many solutions.