the orientation of the parabolas can easily be found by analysing the power of x and y and their signs. if x is squared , parabola opens up and also if its coefficient is negative it opens down. if y is squared , the parabola opens right and also if its coefficient is negative it opens left. however in order to do the above analysis our equation must be in standard form .
our parabola is
which is not standard form of any parabola . hence we square on both hand side and convert it into standard form.
hence we see that x is squared and its coefficient is non negative . there for it opens up.
Option A: Up
When we have a quadratic equation of the form:
y = ax^2 + bx + c
The sign of "a" defines how the equation "opens"
This is because a is multiplicating the term that grows faster as x changes (the biggest power in the polynomial, x^2)
So if a is positive, as IxI grows, the value of y(x) will be also positive.
if a is negative, as IxI grows the value of y(x) will also be negative.
So here we have the equation y = x^2
here we have a = 1, b = 0 and c = 0.
Here "a" is positive, this means that the parabola will open up, so the correct option is A.
The parabola will open upwards.
the squared variable is the "x", therefore is a vertical parabola, the coefficient of the x² is positive, so it opens upwards, like a cup.