Answer:
a) -2, 1 and 2
b) 4
Step-by-step explanation:
The given equation is:
g(x) = (x + 2)(x - 1)(x - 2)
Part a1 and a2) Finding zeros of the function
By zeroes of the function we mean the points the graph where the value of the function is zero. In order to find the zeroes of the function we equate the function equation to zero and find the corresponding values of x. This is shown below:
0 = (x + 2)(x - 1)(x - 2)
According to the zero product property, we can write:
x + 2 = 0 ⇒ x = -2
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
Therefore, the zeroes of the given function are -2, 1 and 2. In ordered pairs we can write these as (-2, 0), (1, 0) and (2, 0)
Part b1 and b2) y-intercept of the function
y-intercept is the point on the graph where the function crosses the y-axis. Since on y-axis, the value of x coordinate is zero, in order to find the y-intercept we simply substitute zero for all occurrences of x. This is shown below:
g(0) = (0 + 2)(0 - 1)(0 - 2)
g(0) = 2(-1)(-2)
g(0) = 4
Thus, the y-intercept of the function is 4, which in ordered pair can be written as (0, 4)
Part c) End behavior of the graph
End behavior of the graph depends on:
- Sign of the leading coefficient
- Degree of the function
Degree of the function is 3 i.e. odd and sign of leading coefficient is positive. This means the end behavior of the graph will be:
- Rising towards Right end
- Falling towards Left end
Part d) Graph of polynomial
Based on all the above discussion, a graph of the function can be plotted. The graph is attached below.
