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

Find the y y -coordinate of the y y -intercept of the polynomial function defined below.\newlinef(x)=−2x(x+2) f(x)=-2 x(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)=−2x(x+2) f(x)=-2 x(x+2) \newlineAnswer:
  1. Evaluate at x=0x = 0: To find the y-coordinate of the y-intercept of the function f(x)=−2x(x+2)f(x) = -2x(x + 2), we need to evaluate the function at x=0x = 0, because the y-intercept occurs where the graph of the function crosses the y-axis, and the x-coordinate of any point on the y-axis is 00.
  2. Substitute x=0x = 0: Substitute x=0x = 0 into the function f(x)=−2x(x+2)f(x) = -2x(x + 2) to find the y-coordinate of the y-intercept.\newlinef(0)=−2×0×(0+2)f(0) = -2 \times 0 \times (0 + 2)
  3. Simplify the expression: Simplify the expression by performing the multiplication.\newlinef(0)=−2×0×2f(0) = -2 \times 0 \times 2\newlinef(0)=0f(0) = 0
  4. Final y-coordinate: Since f(0)=0f(0) = 0, the y-coordinate of the y-intercept is 00.

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