Definition: A zero of a function is an input value x for which f(x) = 0; on the graph, it is a point where the curve meets the x-axis.
What is a zero?
It is a solution of the equation f(x) = 0. Zeros are also called roots, and the matching points (c, 0) are the x-intercepts. Finding them answers questions such as: when does the ball reach the ground?
How do you find zeros?
Set the formula equal to zero and solve. For a quadratic, you can factor, complete the square, or use the quadratic formula. On a graph, read where the curve crosses the horizontal axis.
Example. Find the zeros of f(x) = x2 – 2x – 15. Factor: (x – 5)(x + 3) = 0. So x = 5 or x = -3. Check: f(5) = 25 – 10 – 15 = 0 and f(-3) = 9 + 6 – 15 = 0.
What do learners confuse?
Zeros are x-values, not y-values. The zero of f(x) = 4x – 12 is 3, not -12. A function may have no real zeros, such as x2 + 4, or several. A repeated zero touches the axis without crossing it.