Question

Define $x$ – intercept of a quadratic equation.
(A) It is a point on the graph where $y$ is zero.
(B) It is a point on the graph where $x$ is zero.
(C) It is a vertical line which divides a graph into two mirror-image halves.
(D) It is a horizontal line which divides a graph into two mirror-image halves.

Answer 1

Hint: $x - $intercept is a point at which the graph intersects X-axis. Take any quadratic equation and draw its graph. Then compare the graph with the options to check which options satisfy the condition of $x - $intercept.

Complete step-by-step answer:
Observe the diagram

Given above is the diagram of a quadratic equation
$\Rightarrow y = a{x^2} + bx + c = 0,a > 0$
This diagram of quadratic equations is called parabola.
In this diagram,
A and B are called $x - $intercepts of the parabola.
V is called the vertex of the parabola.
And the line passing through V is called the axis of the parabola because the graph of the parabola is symmetric to both the sides of the axis.
So, option (D) It is a horizontal line which divides a graph into two mirror-image halves, is incorrect because there is no horizontal line that divides the parabola into two mirror-image halves.
Option (C) It is a vertical line which divides a graph into two mirror-image halves, is incorrect because the vertical line which divides a graph into two mirror-image halves is called the axis of the parabola.
Option (B) It is a point on the graph where $x$ is zero, is incorrect because it is called the $y - $intercept
Thus, from the above explanation, the correct answer is, option (A) It is a point on the graph where $y$ is zero.
So, the correct answer is “Option A”.

Note: This was more of a reasoning question than of calculation. For this question, you need to have a good visualization skill and you need to know the meanings of the mathematical terms. If you know that the $x - $intercept is the point where a graph intersects the X-axis then it is easy to understand that, at that point the value of $y$ will be equal to zero.