ExplanationHere we have been given a parabola symmetric along x axis.
General Equation of parabola is : \(y^2=ax+b\) So rewrititng this equation in the form of quantities we can say:
\(x=\frac{1}{a}y^2 -\frac{b}{a}\)
Hence the two qty are equal when \(a=-1\) and \(\frac{b}{a}=-1\) or \(b=1\)
Now in order to calculate two variables namely \(a\) and \(b\) we need two eaquations. We can get one equation by putting the point (-1, 0) in the parabola equation \(y^2=ax+b\).
Hence we cannot say if the answer is C or not!Depending upon the second point of the parabola the quantities may or maynot be equal.
Hence D is the answer. Next, the parabola equation if it was sym. on the y axis is \(y^2=a(x-h)+K\) , while k and h are vertex points. Can we say for the parabola symmetric to x-axis that it is \(x^2=a(y-h)+K\)?