Graph the function by first finding its zeroes. y = x3- 2x2 + x
1 answer:
Answer:
The zeros of the function are;
x = 0 and x = 1
Step-by-step 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;
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Answer: Third option:
Step-by-step explanation:
The equation in Slope Intercept form of a line that does not pass through the point (0,0), which is known as "Origin, is the following:
Where "m" is the slope of the line and "b" is the y-intercept.
The equation in Slope Intercept form of a line that passes through the Origin, is:
Where "m" is the slope of the line.
In this case you can observe in the picture attached that the line passes through the point (0,0).
You can also notice that "y" would be the Dependent variable and "x" the Independent variable.
Therefore, the equation of this must have this form:
The only equation that matches with that form, is the one given in the Third option. This is: