Question

How do I find the y intercept of a parabola?

Answer 1

In the given question, we are required to figure out a way to find the y intercept of a parabola. Y intercept means the point on the y axis where the parabola meets the y axis. There can be various types of orientations of a parabola such as vertical parabola, horizontal parabola along the coordinate axes and having the vertex at origin and shifted parabola where the vertex of parabola is shifted to some point other than origin.

Complete step by step solution: Let us assume the equation of the parabola discussed is $y = \left( {a{x^2} + bx + c} \right)$. This equation represents a parabola that has vertical orientation and has vertex shifted to some point other than origin. So, we have to figure out a way to find the y intercept for the required parabola. Y intercept means the point on the y axis where the parabola meets the y axis. We know that the x coordinate for any point on y axis is zero. Hence, we find the y intercept of a parabola by equating the value of x as zero in the equation of parabola and finding the corresponding value of x.
Putting $x = 0$ in the equation of the parabola $y = \left( {a{x^2} + bx + c} \right)$, we get $y = c$.
Hence, we get the intercept of the assumed parabola as $\left( {0,c} \right)$.

Note: The vertex of a parabola is the turning point of the curve. Y intercept of a parabola can also be found by sketching the curve and finding out the point where the parabola cuts the y axis. There may be multiple y intercepts of a parabola as well.