Maths-

General

Easy

Question

# y=x^{2 }- a

In the equation above, a is a positive constant and the graph of the equation in the xy‑plane is a parabola. Which of the following is an equivalent form of the equation?

## The correct answer is:

### We have given the equation y = x^{2 }– a

The given equation can be thought of as the difference of two squares,

where one square is *x*^{2} and the other square is *a.*

*We know that , a*^{2}-b^{2}= (a + b) (a-b) ,

Using this difference of squares formula,

Simplifying it we get,

Options A, C, and D are incorrect because they are not equivalent to the given equation.

Option A is incorrect because it is equivalent to *y *= *x*^{2 }− *a*^{2 }.

Option C is incorrect because it is equivalent to y = x^{2} – (a^{2}/4).

Option D is incorrect because it is equivalent to *y *= *x*^{2} + 2*ax *+ *a*^{2}.

^{2}-b

^{2}= (a + b) (a-b) ,

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