For the following exercises, use the given information about the polynomial graph to write the equation. Double zero at x = −3 and triple zero at x = 0. Passes through the point (1, 32).

Copy and complete the anticipation guide in your notes. StatementThe quadratic formula can only be used when solving a quadratic equation.Cubic equations always have three real roots.The graph of a cubic function always passes through all four quadrants.The graphs of all polynomial functions must pass through at least two quadrants.The expression $x2>4$ is only true if $x>2$.If you know the instantaneous rates of change for a function at $x=2$ and $x=3$, you can predict fairly well what the function looks like in between.
Agree Disagree Justification
Statement
The quadratic formula can only be used when solving a quadratic equation. Cubic equations always have three real roots. The graph of a cubic function always passes through all four quadrants. The graphs of all polynomial functions must pass through at least two quadrants.
The expression $x2>4$ is only true if $x>2$. If you know the instantaneous rates of change for a function at $x=2$ and $x=3$, you can predict fairly well what the function looks like in between.

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 5. Roots of multiplicity 2 at $x=minus;3$ and $x=2$ and a root of multiplicity 1 at $x=minus;2$. y-intercept at (0, 4).

Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros: $P(x)=a(x-\alpha )(x-\beta )(x-\gamma ),a\ne 0$
Type 2: Two real zeros, one repeated: $P(x)=a(x-\alpha )2(x-\beta ),a\ne 0$
Type 3: One real zero repeated three times: $P(x)=a(x-\alpha )3,a\ne 0$

Type 4: One real and two imaginary zeros: $P(x)=(x-\alpha )(ax2+bx+c),\mathrm{△}=b2-4ac<0,a\ne 0$
Experiment with the graphs of Type 4 cubics. What is the geometrical significance of $\alpha \alpha$ and the quadratic factor which has imaginary zeros?