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Concept explainers
To describe: the leading coefficient and degree of the polynomial function using the graph.
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Answer to Problem 21E
Degree is odd and leading coefficient is negative.
Explanation of Solution
Given information:
A graph is given as
Concept used:
A polynomial function is of the form
Terms of a polynomial function should be arranged in descending order according to its degree to express it in a standard form and degree of each term should be a positive integer or whole number. The coefficients should be real numbers.
Leading coefficient of a polynomial function is the coefficient of the leading term.
Degree of the polynomial is the degree of leading term or the height degree in the polynomial function.
For the polynomial
The end behavior can describe the graph of a polynomial function as
The end behavior of a polynomial function can be determined by the leading coefficient and the degree of the polynomial.
If degree is even and leading coefficient is negative.
If degree is odd and leading coefficient is negative.
If degree is odd and leading coefficient is positive.
If degree is even and leading coefficient is positive.
Calculation:
Consider the given graph of polynomial function.
From the graph it can be concluded that
Hence, degree is odd and leading coefficient is negative.
Chapter 4 Solutions
Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
- Write a quadratic equation in factored form that has solutions of x = 2 and x = = -3/5 ○ a) (x-2)(5x + 3) = 0 ○ b) (x + 2)(3x-5) = 0 O c) (x + 2)(5x -3) = 0 ○ d) (x-2)(3x + 5) = 0arrow_forwardA vacant lot is being converted into a community garden. The garden and a walkway around its perimeter have an area of 690 square feet. Find the width of the walkway (x) if the garden measures 14 feet wide by 18 feet long. Write answer to 2 decimal places. (Write the number without units). Hint: add 2x to each of the garden dimensions of 14 x 18 feet to get the total area for the length multiplied by width.arrow_forwardSolve x-1 x+2 = 12 3 4 Your Answer: Answerarrow_forward
- Find the solutions to the following equation 21x²+5x=6 ○ a) -3/7, 3/2 ☐ b) -2/3, 3/7 ○ c) -7/3, 3/2 ○ d) -2/3, 7/3arrow_forwardListen Solve the quadratic equation. Write the one solution, do not write x =. 2 x²+6x+9= 0 বarrow_forwardSolve the rational equation 14 1 + x-6 x x-7 x-7 ○ a) x = 1, x = 8 ○ b) x = 1 ○ c) x = 7 ○ d) x = 1, x = 7arrow_forward
- Solve the absolute inequality | x + 5 > 3 ○ a) (-∞, -8] U[-2, ∞0) ☐ b) (-8, -2) c) (-2, ∞0) ○ d) (-∞, - 8) U(-2, ∞0)arrow_forward1) Listen Describe the error in the problem X 3 X x 3 - 2 = 25x = 0 25x 25 x = ±5arrow_forwardA falling object travels a distance given by the formula d = 6t + 7t² where d is in feet and t is the time in seconds. How many seconds will it take for the object to travel 115 feet? Round answer to 2 decimal places. (Write the number, not the units). Your Answer:arrow_forward
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