Please check my answers.
Find the y-intercept of the polynomial function.
f(x) = -x2 - 2x + 8
I got:y=8
f(x) = (x + 1)(x - 6)(x - 1)2
I got: y=-6
f(x) = -x2(x + 6)(x2 - 1)
I got:y=0
all correct.
correct
Let's check your answers one by one:
1. For the polynomial function f(x) = -x^2 - 2x + 8, the y-intercept is the value of y when x = 0.
Substitute x = 0 in the function:
f(0) = -(0)^2 - 2(0) + 8
f(0) = -0 + 0 + 8
f(0) = 8
So, your answer of y = 8 is correct.
2. For the polynomial function f(x) = (x + 1)(x - 6)(x - 1)^2, the y-intercept is the value of y when x = 0.
Substitute x = 0 in the function:
f(0) = (0 + 1)(0 - 6)(0 - 1)^2
f(0) = (1)(-6)(1)^2
f(0) = -6
So, your answer of y = -6 is correct.
3. For the polynomial function f(x) = -x^2(x + 6)(x^2 - 1), the y-intercept is the value of y when x = 0.
Substitute x = 0 in the function:
f(0) = -(0)^2(0 + 6)(0^2 - 1)
f(0) = -0(6)(-1)
f(0) = 0
So, your answer of y = 0 is correct.
All your answers are correct. Well done!
To find the y-intercept of a polynomial function, you need to substitute x with 0 in the function and determine the value of y.
Let's check your answers:
1. f(x) = -x^2 - 2x + 8
To find the y-intercept, substitute x with 0:
f(0) = -(0)^2 - 2(0) + 8
f(0) = 0 + 0 + 8
f(0) = 8
Your answer of y = 8 is correct.
2. f(x) = (x + 1)(x - 6)(x - 1)^2
To find the y-intercept, substitute x with 0:
f(0) = (0 + 1)(0 - 6)(0 - 1)^2
f(0) = (1)(-6)(-1)^2
f(0) = -6
Your answer of y = -6 is incorrect. The correct y-intercept is y = 0.
3. f(x) = -x^2(x + 6)(x^2 - 1)
To find the y-intercept, substitute x with 0:
f(0) = -(0)^2(0 + 6)(0^2 - 1)
f(0) = 0
Your answer of y = 0 is correct.
So, to summarize, the correct y-intercepts are:
1. f(x) = -x^2 - 2x + 8 : y = 8
2. f(x) = (x + 1)(x - 6)(x - 1)^2 : y = 0
3. f(x) = -x^2(x + 6)(x^2 - 1) : y = 0