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Question

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The diagram shows a graph with equation $y=ax^3+bx^2+cx+d$, where $a$, $b$, $c$, and $d$ are real constants.

The graph passes through the points $(-6,0)$ and $(-2,32)$ and touches the $x$-axis at the point $(6,0)$.

A student attempts to find the equation of the curve, and writes the following working:
$\boxed {y=(x+6)(x-6)^2 \\ y=(x+6)(x^2-12x+36) \\ y=x^3-6x^2-36x+216}$

a) Explain the mistake the student has made.

b) Find the correct equation of the curve.

mku
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  • What you think, student may forget about a coefficient. – Lion Heart Oct 23 '21 at 14:12
  • I have no idea how to do this question. I can see that the student is assuming that a (the coefficient of x cubed) is 1. However, I don't know what else to do. I have tried to use the 3 co-ordinates that the curve passes through but then I am stuck. – mku Oct 23 '21 at 14:15
  • Coefficient of function? Then you can fix y-values. – Lion Heart Oct 23 '21 at 14:19

1 Answers1

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The only thing missing is something that you have mentioned: the coefficient $a$. It is clear that $y=a(x+6)(x-6)^2$ and then $x=-2\implies y=256a$. So, $a$ should be equal to $\frac18$.

José Carlos Santos
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