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Find the y-coordinate of the y-intercept of the polynomial function defined below. f(x)=-8x^(3)-5+8x+2x^(2) Answer:

Find the y y -coordinate of the y y -intercept of the polynomial function defined below.\newlinef(x)=−8x3−5+8x+2x2 f(x)=-8 x^{3}-5+8 x+2 x^{2} \newlineAnswer:

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Q. Find the y y -coordinate of the y y -intercept of the polynomial function defined below.\newlinef(x)=−8x3−5+8x+2x2 f(x)=-8 x^{3}-5+8 x+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)=−8x3−5+8x+2x2f(x) = -8x^{3} - 5 + 8x + 2x^{2}.\newlinef(0)=−8(0)3−5+8(0)+2(0)2f(0) = -8(0)^{3} - 5 + 8(0) + 2(0)^{2}
  3. Simplify expression: Simplify the expression by calculating the value of each term with x=0x = 0.\newlinef(0)=−8(0)−5+8(0)+2(0)f(0) = -8(0) - 5 + 8(0) + 2(0)\newlinef(0)=0−5+0+0f(0) = 0 - 5 + 0 + 0\newlinef(0)=−5f(0) = -5
  4. Find y-coordinate: The y-coordinate of the y-intercept is the value of f(0)f(0), which we have found to be −5-5.

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