What is the Y-intercept?

Question

In class, my math teacher was teaching us how to draw functions on a coordinate plane, and he mentioned something about the Y-Intercept being an important step in creating/solving a function. But, what exactly is a Y-Intercept?

Answer 1

The $y$-intercept of a function $f(x)$ is the point where the function intersects the $y$-axis (if in fact it does intersect the $y$-axis) and it is found by evaluating $f(0)$, i.e., finding the value of $f(x)$ when $x = 0$.

For example,

• the line $f(x) = y = 3x + 2$ intersects the $x$-axis at when $x = 0$:
  when $\;y = 3\cdot 0 + 2 = 2$. This is the function's y-intercept.

• The parabola $f(x) = y = 2x^2 + 8$ intersects the $y$-axis when $x = 0:\;$
  when $\;y = 2(0)^2 + 8 = 8$. This is the function's y-intercept.