Find the y-coordinate of the y-intercept of the polynomial function defined below.f, of, x, equals, 2, left bracket, x, squared, minus, 2, right bracket, left bracket, x, plus, 5, right bracket, left bracket, x, squared, minus, 1, right bracket, cubedf(x)=2(x 2 −2)(x+5)(x 2 −1) 3
Question
Find the y-coordinate of the y-intercept of the polynomial function defined below.f, of, x, equals, 2, left bracket, x, squared, minus, 2, right bracket, left bracket, x, plus, 5, right bracket, left bracket, x, squared, minus, 1, right bracket, cubedf(x)=2(x 2 −2)(x+5)(x 2 −1) 3
Solution
The y-intercept of a function is the point where the graph of the function intersects the y-axis. This happens when x = 0.
So, to find the y-coordinate of the y-intercept of the function f(x) = 2(x^2 - 2)(x + 5)(x^2 - 1)^3, we substitute x = 0 into the function:
f(0) = 2(0^2 - 2)(0 + 5)(0^2 - 1)^3 = 2(-2)(5)(-1)^3 = 2*(-2)5(-1) = 20
So, the y-coordinate of the y-intercept of the function is 20.
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