Which of the following graphs is a polynomial function with x-intercepts of (-3,0)(-1,0), and (2,0)?
2 answers:
The intercepts of the third degree polynomial corresponds to the zeros of the equation
y = d*(x-a)*(x-b)(x-c)
Where a, b and c are the roots of the polynomial and d an adjustment coefficient.
y = d*(x+2)*(x)*(x-3)
Lets assume d = 1, and we get
y = (x+2)*(x)*(x-3) = x^3 - x^2 - 6x
We graph the equation in the attached file.
y = d*(x-a)*(x-b)(x-c)
Where a, b and c are the roots of the polynomial and d an adjustment coefficient.
y = d*(x+2)*(x)*(x-3)
Lets assume d = 1, and we get
y = (x+2)*(x)*(x-3) = x^3 - x^2 - 6x
We graph the equation in the attached file.
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Answer:
20. x = 5, y = -2
21. x = 11, y = 12
22. x = 22, y = 11
23. x = 11, y = 10
Step-by-step explanation:
20. Opposite sides in the parallelogram are congruent, so
Solve this system of two equations:
Multiply the first equation by 2 and add two equations:
Substitute it into the first equation:
21. Opposite angles in the parallelogram are congruent, so
Consecutive angles are supplementary, so
Solve this system of two equations:
From the second equation
Substitute it into the first equation:
22. Opposite angles in the parallelogram are congruent, so
Consecutive angles are supplementary, so
Solve this system of two equations:
From the first equation
Substitute it into the second equation:
23. Opposite sides in the parallelogram are congruent, so
Solve this system of two equations:
Multiply the second equation by 2 and subtract it from the first equation:
Substitute it into the first equation: