Jan. 18, 1996   Math 311,   Quiz 1

Let $\Gamma(t)=\left(at^2+bt+c,dt+e\right)$, where $t$ is the independent variable and the constants a, b, c, d, and e are unknown coefficients. 

  1. {5}Is it possible to assign values to the unknown coefficients so
that the curve $\Gamma$ satisfies the  following equations:
$$
\Gamma(0)=(1,2),\quad \Gamma(1)=(4,-3),\quad \Gamma^\prime(0)=(1,1)\,.
$$
If the answer is no, explain why you think it is no, and if it is yes
what are the values that the unknown coefficients must equal? Also if
the answer is yes, plot the curve for $0\leq t \leq 2$.
{3in}


  2. {5}Is it possible to assign values to the unknown coefficients so
that the curve $\Gamma$ satisfies the  following equations:
$$
\Gamma(0)=(1,2),\quad \Gamma(1)=(0,5),\quad \Gamma^\prime(0)=(1,3)\,.
$$
If the answer is no, explain why you think it is no, and if it is yes
what are the values that the unknown coefficients must equal? Also if
the answer is yes, plot the curve for $0\leq t \leq 2$.

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