Complete the table for $y = x^3 - 3x$. $x$ | $-3$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ $y$ | $-18$ | $-2$ | $0$ | $0$ | $-2$ | $18$ | Draw the graph of $y = x^3 - 3x$ for $-3 \leq x \leq 3$. Use your graph to solve $x^3 - 3x = 10$.

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Complete the table for $y = x^3 - 3x$ - OCR - GCSE Maths - Question 9 - 2018 - Paper 1

Question 9

Complete the table for $y = x^3 - 3x$. $x$ | $-3$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ $y$ | $-18$ | $-2$ | $0$ | $0$ | $-2$ | $18$ | Draw the graph of... show full transcript

Worked Solution & Example Answer:Complete the table for $y = x^3 - 3x$ - OCR - GCSE Maths - Question 9 - 2018 - Paper 1

Step 1

Complete the table for $y = x^3 - 3x$.

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Answer

To complete the table, we substitute each value of $x$ into the equation $y = x^3 - 3x$ :

For $x = -3$ : $y = (-3)^3 - 3(-3) = -27 + 9 = -18$
For $x = -2$ :
$y = (-2)^3 - 3(-2) = -8 + 6 = -2$
For $x = -1$ :
$y = (-1)^3 - 3(-1) = -1 + 3 = 2$
For $x = 0$ :
$y = 0^3 - 3(0) = 0$
For $x = 1$ :
$y = 1^3 - 3(1) = 1 - 3 = -2$
For $x = 2$ :
$y = 2^3 - 3(2) = 8 - 6 = 2$
For $x = 3$ :
$y = 3^3 - 3(3) = 27 - 9 = 18$

The completed table is as follows:

$x$ | $-3$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$
$y$ | $-18$ | $-2$ | $2$ | $0$ | $-2$ | $2$ | $18$

Step 2

Draw the graph of $y = x^3 - 3x$ for $-3 \leq x \leq 3$.

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Answer

To draw the graph of the function, plot the points from the completed table:

Plot the points:
$(-3, -18)$ ,
$(-2, -2)$ ,
$(-1, 2)$ ,
$(0, 0)$ ,
$(1, -2)$ ,
$(2, 2)$ ,
$(3, 18)$ .
Connect the points smoothly, noting that the graph will have a cubic curve shape that passes through them while adhering to the established range for $x$ .

Step 3

Use your graph to solve $x^3 - 3x = 10$.

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Answer

To solve the equation $x^3 - 3x = 10$ , first rearrange it to $x^3 - 3x - 10 = 0$ .

Once the graph is drawn, identify where the graph intersects the horizontal line $y = 10$ . This intersection gives the solution(s) for the equation.

From our graph, locate the intersection points:

Approximate the $x$ -values where the graph reaches $y = 10$ , which could be estimated graphically or with numerical methods, providing the roots as necessary.

Complete the table for $y = x^3 - 3x$ - OCR - GCSE Maths - Question 9 - 2018 - Paper 1

Worked Solution & Example Answer:Complete the table for $y = x^3 - 3x$ - OCR - GCSE Maths - Question 9 - 2018 - Paper 1

Complete the table for $y = x^3 - 3x$.

Draw the graph of $y = x^3 - 3x$ for $-3 \leq x \leq 3$.

Use your graph to solve $x^3 - 3x = 10$.

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