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

Find the y y -coordinate of the y y -intercept of the polynomial function defined below.\newlinef(x)=−2x2−5x+2x3−3 f(x)=-2 x^{2}-5 x+2 x^{3}-3 \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)=−2x2−5x+2x3−3 f(x)=-2 x^{2}-5 x+2 x^{3}-3 \newlineAnswer:
  1. Evaluate at x=0x=0: To find the yy-coordinate of the yy-intercept of the function f(x)=−2x2−5x+2x3−3f(x) = -2x^2 - 5x + 2x^3 - 3, 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, and the xx-coordinate of any point on the yy-axis is 00.
  2. Substitute x=0x=0: Substitute x=0x = 0 into the function f(x)=−2x2−5x+2x3−3f(x) = -2x^2 - 5x + 2x^3 - 3 to find the y-coordinate of the y-intercept.\newlinef(0)=−2(0)2−5(0)+2(0)3−3f(0) = -2(0)^2 - 5(0) + 2(0)^3 - 3
  3. Simplify expression: Simplify the expression by performing the calculations.\newlinef(0)=−2(0)−5(0)+2(0)−3f(0) = -2(0) - 5(0) + 2(0) - 3\newlinef(0)=0−0+0−3f(0) = 0 - 0 + 0 - 3\newlinef(0)=−3f(0) = -3
  4. Find y-intercept: The y-coordinate of the y-intercept is the value of f(0)f(0), which we have found to be −3-3.

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