Question

Describe the graph of the function f(x) = x3 − 18x2 + 107x − 210. Include the y-intercept, x-intercepts, and the shape of the graph.

Answer 1

F(x) = x³ - 18x² + 107x - 210

X - Intercept: f(x) = x³ - 18x² + 107x - 210
0 = x³ - 18x³ + 107x - 210
0 = x³ - 7x² - 11x² + 77x + 30x - 210
0 = x²(x) - x²(7) - 11x(x) + 11x(7) + 30(x) - 30(7)
0 = x²(x - 7) - 11x(x - 7) + 30(x - 7)
0 = (x² - 11x + 30)(x - 7)
0 = (x² - 6x - 5x + 30)(x - 7)
0 = (x(x) - x(6) - 5(x) + 5(6))(x - 7)
0 = (x(x - 6) - 5(x - 6))(x - 7)
0 = (x - 5)(x - 6)(x - 7)
0 = x - 5 or 0 = x - 6 or 0 = x - 7
+ 5 + 5 + 6 + 6 + 7 + 7
5 = x or 6 = x or 7 = x
Solution Set: {5, 6, 7}

Y - Intercept: f(x) = x³ - 18x² + 107x - 210
f(x) = (0)³ - 18(0)² + 108(0) - 210)
f(x) = 0 - 18(0) + 0 - 210
f(x) = 0 - 0 - 210
f(x) = 0 - 210
f(x) = -210

Answer 2

I'm kind of confused. Can you send me a message of the answer I should input?