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Find the y-coordinate of the y-intercept of the polynomial function defined below. f(x)=-x^(3)-8x+3-4x^(4)+2x^(2) Answer:

Find the y y -coordinate of the y y -intercept of the polynomial function defined below.\newlinef(x)=−x3−8x+3−4x4+2x2 f(x)=-x^{3}-8 x+3-4 x^{4}+2 x^{2} \newlineAnswer:

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Full solution

Q. Find the y y -coordinate of the y y -intercept of the polynomial function defined below.\newlinef(x)=−x3−8x+3−4x4+2x2 f(x)=-x^{3}-8 x+3-4 x^{4}+2 x^{2} \newlineAnswer:
  1. Evaluate at x=0x = 0: To find the yy-coordinate of the yy-intercept of the function f(x)f(x), we need to evaluate f(x)f(x) at x=0x = 0, because the yy-intercept occurs where the graph of the function crosses the yy-axis, and the xx-coordinate of any point on the yy-axis is yy00.
  2. Substitute x=0x = 0: Substitute x=0x = 0 into the polynomial function f(x)=−x3−8x+3−4x4+2x2f(x) = -x^3 - 8x + 3 - 4x^4 + 2x^2.\newlinef(0)=−(0)3−8×(0)+3−4×(0)4+2×(0)2f(0) = -(0)^3 - 8\times(0) + 3 - 4\times(0)^4 + 2\times(0)^2
  3. Simplify the expression: Simplify the expression by performing the operations. f(0)=−0−0+3−0+0f(0) = -0 - 0 + 3 - 0 + 0
  4. Combine terms: Combine all the terms to find the value of f(0)f(0).f(0)=3f(0) = 3
  5. Find y-intercept: The y-coordinate of the y-intercept is the value of f(0)f(0), which we have found to be 33.

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