Find the y-coordinate of the y-intercept of the polynomial function defined below.f, of, x, equals, minus, x, left bracket, x, minus, 3, right bracket, squared, left bracket, 2, x, minus, 2, right bracket, left bracket, x, plus, 2, right bracketf(x)=−x(x−3) 2 (2x−2)(x+2)
Question
Find the y-coordinate of the y-intercept of the polynomial function defined below.f, of, x, equals, minus, x, left bracket, x, minus, 3, right bracket, squared, left bracket, 2, x, minus, 2, right bracket, left bracket, x, plus, 2, right bracketf(x)=−x(x−3) 2 (2x−2)(x+2)
Solution
The y-intercept of a function is the point where the graph of the function intersects the y-axis. This occurs when the x-value is 0.
So, to find the y-coordinate of the y-intercept for the function f(x) = -x(x-3)^2(2x-2)(x+2), we substitute x = 0 into the function:
f(0) = -0 * (0-3)^2 * (2*0-2) * (0+2)
Solving this gives:
f(0) = -0 * 9 * -2 * 2
f(0) = 0
So, the y-coordinate of the y-intercept of the function is 0.
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