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

Find the y y -coordinate of the y y -intercept of the polynomial function defined below.\newlinef(x)=−8x3+3x2+4x f(x)=-8 x^{3}+3 x^{2}+4 x \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)=−8x3+3x2+4x f(x)=-8 x^{3}+3 x^{2}+4 x \newlineAnswer:
  1. Evaluate at x=0x = 0: To find the yy-coordinate of the yy-intercept of the function, we need to evaluate the function at x=0x = 0, because the yy-intercept occurs where the graph of the function crosses the yy-axis.
  2. Substitute into function: Substitute x=0x = 0 into the polynomial function f(x)=−8x3+3x2+4xf(x) = -8x^3 + 3x^2 + 4x.f(0)=−8(0)3+3(0)2+4(0)f(0) = -8(0)^3 + 3(0)^2 + 4(0)
  3. Simplify expression: Simplify the expression by calculating the powers and products.\newlinef(0)=−8(0)+3(0)+4(0)f(0) = -8(0) + 3(0) + 4(0)\newlinef(0)=0+0+0f(0) = 0 + 0 + 0
  4. Final result: The result of the calculation is 00, which means the yy-coordinate of the yy-intercept is 00.\newlinef(0)=0f(0) = 0

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