Question

Find the y-coordinate of the y-intercept of the polynomial function defined below:

f(a) = x(x + 6)(x^2 + 1)(52 - 3)
A) 0
B) -312
C) 312
D) -62

Answer 1

The y-coordinate of the y-intercept for the given polynomial function is 0, as when you substitute x with 0, the function's value results in 0 due to multiplication with the first term which is zero.

Step-by-step explanation:

To find the y-coordinate of the y-intercept of the given polynomial function f(x) = x(x + 6)(x^2 + 1)(52 - 3), we need to determine the function's value when x is zero. The y-intercept of a function occurs where the function crosses the y-axis, which is when x is zero (x=0). Substituting 0 into the polynomial gives:

f(0) = 0(0 + 6)(0^2 + 1)(52 - 3)

Now, calculate the values inside each parenthesis:

• The first term is 0, so the entire product will be zero.
• The second term, when x is 0 is (0 + 6), which equals 6.
• For the third term, (0^2 + 1) is 1.
• Finally, (52 - 3) simplifies to 49.

So the calculation simplifies to:

f(0) = 0 * 6 * 1 * 49 = 0

Since the entire expression is multiplied by zero, the result is zero, meaning the y-coordinate of the y-intercept is 0.