Question

How do I find $x -$ intercepts of a parabola?

Answer 1

Here we need to know that general equation of the parabola is $y = a{x^2} + bx + c$ and whenever we need to find the $x -$intercepts it means that we need to find the point where this parabola cuts the $x -$axis. Hence we need to just insert $y = 0$ and get the value of the intercept on $x -$ axis required.

Complete step by step solution:
Here we are given to find the $x -$intercepts of the curve which is given as parabola. So here we need to know that general equation of the parabola is given as $y = a{x^2} + bx + c$ and we need to find the points where this parabola meets the $x -$axis
We know that on the $x -$axis every value of $y = 0$
Hence to get the $x -$intercept we just need to put $y = 0$ in the equation of the curve. This is valid for any curve.
For example: If we have the line also say $2x + 3y = 6$ then its x-intercept will be as $y = 0$
So we will get
$2x + 3(0) = 6 \\\ 2x = 6 \\\ x = 3 \\\$
Hence in the similar way we can put the value of $y = 0$ in the above parabola to get its x-intercept.
Hence putting $y = 0$ we get:
$y = a{x^2} + bx + c$
$a{x^2} + bx + c = 0$
Now we know that it is the quadratic equation and we can solve it by using the formula by which we find the roots of quadratic equation as:
$x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$
Hence in this way we can find the x-intercepts of the parabola.

Note:
Here if the student is given to find the y-intercept then the whole process is the same but the only difference is that we need to put here $x = 0$ and not $y = 0$ as on the y-axis the value of $x = 0$.