Let $y = 2x^3 - x^2 - 10x$.

1. Find the missing table value when $x=2$.

For $x=2$,
$y=2(2)^3-(2)^2-10(2)$
$=16-4-20$
$=-8?$
Check carefully:
$2(2)^3=16,$ so
$16-4-20=-8.$

1. Use the completed table to identify all coordinates to be plotted.

From the completed table,

$(-2,0),\ (-1.5,6),\ (-1,7),\ (-0.5,4.5),\ (0,0),\ (1,-9),\ (1.5,-10.5),\ (2,-12).$

2. Plot the points accurately on the given grid.

Plot each coordinate on the axes, using the given vertical scale marked in units of $2$ and the horizontal values from $x=-2$ to $x=2$.

3. Join the plotted points with a smooth curve over the required interval.

Draw a smooth continuous curve through the plotted points for

$-2\le x\le 2.$

The curve should pass through the origin and continue down to approximately $(2,-12)$ on the right.

1. Relate the given equation to the graph already drawn.

The graph drawn is
$y=2x^3-x^2-10x$.

Given
$2x^3-x^2-5x=-8$,
write
$(2x^3-x^2-10x)+5x=-8$.

So
$y+5x=-8$.

2. Rewrite the equation as a straight line to compare with the curve.

From
$y+5x=-8$,
we get
$y=-5x-8$.

3. Explain why there is only one solution from the graph.

The solutions of the equation are the $x$-coordinates where the curve
$y=2x^3-x^2-10x$
meets the line
$y=-5x-8$.

From the graph, the line meets the curve at only one point, so there is only one solution.

1. Rewrite the equation in a form that can be used with the drawn curve.

The graph drawn is for
$y=2x^3-x^2-10x$.

Given
$2x^3-x^2-5x=-8,$
write
$2x^3-x^2-10x=-5x-8.$
So draw the straight line
$y=-5x-8$
on the same graph and read the $x$-coordinate where it meets the curve.

2. Read the solution from the point of intersection.

From the graph, the line $y=-5x-8$ intersects the curve at approximately
$x=-1.9.$

1. Identify the maximum point on the drawn curve and read its $x$-coordinate.

From the graph of $y=2x^3-x^2-10x$, the maximum point is the highest turning point on the curve. Reading its horizontal position from the graph gives

$x \approx -1.1.$