Which of the following is a polynomial function in standard form with zeros at –8, –1, and 3?
2 answers:
<h2>Answer:</h2>
Option: C is the correct answer.
The polynomial in standard form is:
C)
The standard form of a equation of a polynomial is written as :
We arrange the terms from least to highest power of x.
We know that if a polynomial has roots as:
a, b and c then the equation of the polynomial is given by:
Here we have: a= -8 , b= -1 and c=3
Hence, the equation of the circle is given by:
which on expanding gives:
Hence, the standard equation of the polynomial is:
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The first line through points (-3, 0) and (-4, -1) is the orange line.
The second line, through (1, 1) and (2, -1) is the purple line.
Since they are both shaded below, the intersection of the shaded regions, is the region colored in blue.
Both lines are included, since they are solid lines.
The equation of the first line can be found as follows:
the slope is
, thus, the equation is:
The equation of the second line can be found as follows:
the slope is
,
thus the equation of the second line is :
We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines,
so we write the inequalities so that they do not hold for (0, 4)
line 1:
y≥x+4
4≥0+4=4 is true, so we change the sign and write : y≤x+4
similarly, line 2:
y≤-2x+3
4≤-2*0+3=3, which is not true, so we have the correct direction.
Note that since the lines were solid, we include the equality case:
Answer:
the shaded region is the solution to the system of inequalities:
i) y≤x+4
ii) y≤-2x+3
The second line, through (1, 1) and (2, -1) is the purple line.
Since they are both shaded below, the intersection of the shaded regions, is the region colored in blue.
Both lines are included, since they are solid lines.
The equation of the first line can be found as follows:
the slope is
The equation of the second line can be found as follows:
the slope is
thus the equation of the second line is :
We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines,
so we write the inequalities so that they do not hold for (0, 4)
line 1:
y≥x+4
4≥0+4=4 is true, so we change the sign and write : y≤x+4
similarly, line 2:
y≤-2x+3
4≤-2*0+3=3, which is not true, so we have the correct direction.
Note that since the lines were solid, we include the equality case:
Answer:
the shaded region is the solution to the system of inequalities:
i) y≤x+4
ii) y≤-2x+3