Question

The polynomial function $f(x) = ax^4 - 3x^3 - 63x^2 + 152x - b$ has one of its zeros at $x = 5$ and passes through the point $(-2, -560)$. a) Use the given information to determine the values of $a$ and $b$. b) Use the given information to state one of the factors of $f(x)$. c) Find all the other factors of $f(x)$. d) Use the factors to determine the zeros of $f(x)$. e) Determine the y-intercept of $f(x)$. f) Determine the end behaviours of $f(x)$. g) Use all the characteristics you determined to sketch a possible graph of $f(x)$. Label accurately all important points on the graph. h) Verify your results using Desmos.com. Discuss any differences between the graph and your sketch.

          The polynomial function $f(x) = ax^4 - 3x^3 - 63x^2 + 152x - b$ has one of its zeros at $x = 5$ and passes through the point $(-2, -560)$. 
a) Use the given information to determine the values of $a$ and $b$.
b) Use the given information to state one of the factors of $f(x)$.
c) Find all the other factors of $f(x)$.
d) Use the factors to determine the zeros of $f(x)$.
e) Determine the y-intercept of $f(x)$.
f) Determine the end behaviours of $f(x)$.
g) Use all the characteristics you determined to sketch a possible graph of $f(x)$. Label accurately all important points on the graph.
h) Verify your results using Desmos.com. Discuss any differences between the graph and your sketch.

The polynomial function f(x) = ax^4 - 3x^3 - 63x^2 + 152x - b has one of its zeros at x = 5 and passes through the point (-2, -560).
a) Use the given information to determine the values of a and b.
b) Use the given information to state one of the factors of f(x).
c) Find all the other factors of f(x).
d) Use the factors to determine the zeros of f(x).
e) Determine the y-intercept of f(x).
f) Determine the end behaviours of f(x).
g) Use all the characteristics you determined to sketch a possible graph of f(x). Label accurately all important points on the graph.
h) Verify your results using Desmos.com. Discuss any differences between the graph and your sketch.

Added by Gary F.

Question

Please give Ace some feedback