Complete the table for $y = 9x^3 + 5x^2 - 3x + 1$.
Give your answer correct to 1 decimal place.

$x$	$-1$	$-0.75$	$-0.5$	$-0.25$	$0$	$0.25$	$0.5$	$0.75$	$1.0$
$y$	$0$	$2.3$	$2.6$		$1$	$0.7$	$1.9$	$5.4$	$12$

On the grid, draw the graph of $y = 9x^3 + 5x^2 - 3x + 1$ for $-1 \le x \le 1$. Use your graph to find the solution of the equation $9x^3 + 5x^2 = 3x + 5$. Answer $x =$ ...

1. Substitute $x = -0.25$ into the equation for $y$

$y = 9(-0.25)^3 + 5(-0.25)^2 - 3(-0.25) + 1$

2. Calculate the value and round to 1 decimal place

$y = -0.140625 + 0.3125 + 0.75 + 1 = 1.921875 \approx 1.9$

1. Plot all the points from the table on the given grid

Using the completed table from part (a), plot the coordinates:
$(-1, 0)$
$(-0.75, 2.3)$
$(-0.5, 2.6)$
$(-0.25, 1.9)$
$(0, 1)$
$(0.25, 0.7)$
$(0.5, 1.9)$
$(0.75, 5.4)$
$(1, 12)$

2. Draw a smooth curve through the plotted points

Connect the plotted points with a continuous, smooth curve, ensuring there are no sharp corners and the turning points are rounded.

1. Rearrange the given equation to match the expression for the graphed curve on one side.

$9x^3 + 5x^2 = 3x + 5$
$9x^3 + 5x^2 - 3x - 5 = 0$
$9x^3 + 5x^2 - 3x + 1 - 6 = 0$
$9x^3 + 5x^2 - 3x + 1 = 6$

2. Identify the line to draw and read the solution from the graph.

Draw the horizontal line $y = 6$ on the graph.
The solution is the $x$-coordinate of the point of intersection between the curve $y = 9x^3 + 5x^2 - 3x + 1$ and the line $y = 6$.
From the graph, $x \approx 0.78$.