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What is the y-intercept of the polynomial equation y=x⁴-3x³-2x²+6x² ?

A.(0,6)
B.(0,-3)
C.(0,-5)
D.(0,0)

User Chris Hill
by
8.3k points

1 Answer

6 votes

Final answer:

The y-intercept of the polynomial equation y = x⁴ - 3x³ - 2x² + 6x² is found by evaluating the equation at x = 0, which gives a result of 0. Therefore, the correct y-intercept is D.(0,0).

Step-by-step explanation:

The student's question is about finding the y-intercept of the polynomial equation y = x⁴ - 3x³ - 2x² + 6x². The y-intercept of an equation is the y-value where the graph of the equation intersects the y-axis (where x = 0). To find the y-intercept of the given polynomial, we need to evaluate the equation for x = 0.

Substituting x = 0 into the equation, we get:

y = (0)⁴ - 3(0)³ - 2(0)² + 6(0)² = 0

Every term in this equation becomes zero because they all contain the factor x raised to some power. Hence, the y-intercept of the equation is 0. According to the options provided, the correct answer is D.(0,0).

User Nicksuch
by
9.0k points
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