For the polynomial function find the following: (i) Degree of the polynomial; (ii) All x intercepts; (iii) The y intercept.
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Question

Quizplus · Accepted Answer

(i) The degree of the polynomial is 2 since it is a quadratic function.
(ii) To find the x-intercepts, we set y = 0 and solve for x. Using the quadratic formula, we get x = (-b ± sqrt(b^2 - 4ac))/2a. Plugging in the coefficients of the function, we get x = (1 ± sqrt(10))/2. Therefore, the x-intercepts are (1 + sqrt(10))/2 and (1 - sqrt(10))/2.
(iii) To find the y-intercept, we set x = 0 and solve for y. Plugging in x = 0, we get y = 2. Therefore, the y-intercept is (0, 2). (i) The degree of the polynomial is 2, as the highest power of x is 2.
(ii) To find x intercepts, we set y=0 and solve for x:
0 = -2x^2 + 5x + 3
0 = (x-1)(-2x-3)
x = 1 or x = -3/2
These are the x-intercepts.
(iii) To find the y-intercept, we set x=0:
y = -2(0)^2 +5(0) + 3
y = 3
Therefore, the y-intercept is 3.

For the Polynomial Function Find the Following: (I) Degree of the Polynomial;