XAT 2015 Quant & DI: Quadratic Equations
This question appeared as a part of the quantitative reasoning and data interpretation section of the XAT 2015. Question 8 of a total of 33 questions that appeared in this section in XAT 2015. This one is an easy aptitude / quant question that tests concepts about quadratic equations and the curves that these equations represent.
Question
Find the equation of the graph shown below.
 y = 3x  4
 y = 2x^{2}  40
 x = 2y^{2}  40
 y = 2x^{2} + 3x  19
 x = 2y^{2} + 3y  19
Correct Answer Choice E. x = 2y^{2} + 3y  19
Explanatory Answer

Given Data
In the graph, x and yaxes have been swapped from the conventional ones.
i.e,. horizontal axis has been named yaxis and the vertical axis has been named xaxis.Key Inference
The curve is a parabola.
A parabola will have an equation of the form y = ax^{2} + bx + c
However, in our case, the x and y axes have been swapped.
So, the equation has to be of the form x = ay^{2} + by + cPoints of Interest
To determine which of the equations fits the curve given, we are going to substitute values of x or y from the graph in the equations and check for a match. We need two to three points to determine that. Let us select points where at least one of the coordinates is 0. The points of interest therefore are: When y is around 4, x = 0
 When y is between 2 and 3, x = 0
 When y is 0, x is around 20
What is the approach?
Substitute x = 0 in the choices that match the form of equation stated in the key inference step and see which one matches the data.
Cross check with another value when y = 0.
The choice that matches both conditions is the answer. 
Compute the equation
The equation has to be of the form x = ay^{2} + by + c.
A quick look at the choices tells us that we can eliminate choices A, B, and D.
Choice A is a linear equation. So, it represents a straight line. Rule it out.
Choices B and D are of the form y = ax^{2}. Our axes are swapped. So, choice B can also be ruled out.Choice C: x = 2y^{2} – 40
Substitute y = 4 in the equation.
We get x = 2(4)^{2} – 40 = 32 – 40 = 8.
However, we know that when y = 4, x = 0.So, Choice C cannot be the answer.
Choice E: x = 2y^{2} + 3y – 19
When y = 4, x = 2(4)^{2} +3(4) – 19 = 32 – 31 = 1.
So, when y is around 4, it will be 0.Let us validate it with one more data point.
When y = 0, x = 2(0)^{2} + 3(0) – 19 = 19.
The value of x is around 20 as indicated in the curve.The correct answer is Choice E.
Video Explanation
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 Number Theory
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