Find the y-coordinate of the y-intercept of the polynomial function defined below.f, of, x, equals, left bracket, x, plus, 3, right bracket, left bracket, 3, x, squared, minus, 5, right bracket, left bracket, x, plus, 4, right bracketf(x)=(x+3)(3x 2 −5)(x+4)
Question
Find the y-coordinate of the y-intercept of the polynomial function defined below.f, of, x, equals, left bracket, x, plus, 3, right bracket, left bracket, 3, x, squared, minus, 5, right bracket, left bracket, x, plus, 4, right bracketf(x)=(x+3)(3x 2 −5)(x+4)
Solution
The y-intercept of a function is the point where the graph of the function intersects the y-axis. This always occurs when the x-value is 0.
So, to find the y-intercept of the function f(x) = (x+3)(3x^2 -5)(x+4), we substitute x = 0 into the function:
f(0) = (0+3)(3*0^2 -5)(0+4)
= (3)(-5)(4)
= -60
So, the y-coordinate of the y-intercept of the function is -60.
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