Question

Graph the function by first finding its zeroes.
y = x3- 2x2 + x

Answer 1

The zeros of the function are;

x = 0 and x = 1

Explanation:

The zeroes of the function simply imply that we find the values of x for which the corresponding value of y is 0.

We let y be 0 in the given equation;

y = x^3 - 2x^2 + x

x^3 - 2x^2 + x = 0

We factor out x since x appears in each term on the Left Hand Side;

x ( x^2 - 2x + 1) = 0

This implies that either;

x = 0 or

x^2 - 2x + 1 = 0

We can factorize the equation on the Left Hand Side by determining two numbers whose product is 1 and whose sum is -2. The two numbers by trial and error are found to be -1 and -1. We then replace the middle term by these two numbers;

x^2 -x -x +1 = 0

x(x-1) -1(x-1) = 0

(x-1)(x-1) = 0

x-1 = 0

x = 1

Therefore, the zeros of the function are;

x = 0 and x = 1

The graph of the function is as shown in the attachment below;