# Root of a function

Definition: A root of a function is an x-value at which the y-value is zero.

Rules:

• Let y=f(x) be a function. Then x=a is a root if f(a)=0 .
• If x=a is a root of f(x) , then the graph of f(x) crosses the x-axis at a.
• So a root is an
• The x-axis is also the line y=0. So substituting y=0 and solving for x gives roots.
 Example: Find the roots of the quadratic function f(x)= x^2-x-2 . To find the roots of a quadratic function, we use the quadratic formula. The roots are: x_1=2    and    x_2=-1 That is, this function crosses the x-axis at 2 points: (2,0) and (-1,0).

 y=-x+2 y=-x^2+2x-1 y=2^x f(x)=sinx 1 root 1 roots 0 roots infinitely many roots root: x=2 root: x=1 - roots: \left\{ {x|x = k\pi ,\,\,k \in \bf{Z}} \right\}

Related topics:

(:commentbox:)