I am doing some examination practice, and I've faced the following question:
Another particular solution which satisfies $y = 1$ and $\frac {dy}{dx} = 0$ when $t = 0$, has equation $y = (1 – 3t + 2t^{2})e^{3t}$ For this particular solution draw a sketch graph of y against t, showing where the graph crosses the t-axis.
However I am having trouble drawing the graph. I know how to draw the two parts individually but the only thing I can think of when drawing $y = (1 – 3t + 2t^{2})e^{3t}$ is that $(1 – 3t + 2t^{2})$ will grow exponentially bigger every time.
What method or thinking strategy can I use to draw that graph?
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