The table gives some values of $x$ and the corresponding values of $y$, correct to one decimal p

Question

The table gives some values of $x$ and the corresponding values of $y$, correct to one decimal place, where $y=\frac{{{x}^{3}}}{6}-x+2$. $x$ $-4$ $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$ $4$ $y$ $-4.7$ $p$ $2.7$ $2.8$ $2$ $1.2$ $1.3$ $3.5$ $8.7$ Find the value of $p$. Using a scale of $2$ cm to represent $1$ unit, draw a horizontal $x$-axis for $-4\le x\le 4$. Using a scale of $1$ cm to represent $1$ unit, draw a vertical $y$-axis for$-5\le y\le 9$. On your axes, plot the points given in the table and join them with a smooth curve. Use your graph to find the solution of $\frac{{{x}^{3}}}{6}-x=-5$. By drawing a tangent, find the gradient of the curve at the point where $x=3$. On the axes used in part (b), draw the graph of the straight line $y+2x=-1\mathrm{ }$ for $-4\le x\le 4$. Write down the $x$ coordinate of the point at which the two graphs intersect. Find the equation, in the form $a{{x}^{3}}+b{{x}^{2}}+cx+d=0$, which is satisfied by the values of $x$ found in part (f)(i).

Accepted Answer

(a) $0.5$. (c) $-3.75$. (d) About $3.5$. (f)(i) $-1.88$; (ii) $x^3+6x+18=0$.

Graphical Solution of a Cubic Equation and Its Applications

Graphical Solution of a Cubic Equation and Its Applications

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