Complete the table for $y = x^3 - 3x$ - OCR - GCSE Maths - Question 9 - 2018 - Paper 1
Question 9
Complete the table for $y = x^3 - 3x$.
$x$ $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$
$y$ $-18$ $-2$ $0$ $0$ $-2$ $18$ $18$
Draw the graph... 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 for the function y=x3−3x, we substitute the given values of x into the equation to find the corresponding values of y.
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=03−3(0)=0
For x=1: y=13−3(1)=1−3=−2
For x=2: y=23−3(2)=8−6=2
For x=3: y=33−3(3)=27−9=18
Thus, the completed table is:
x−3−2−10123 y−18−220−2218
Step 2
Draw the graph of $y = x^3 - 3x$ for $-3 < x < 3$
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Answer
To draw the graph of the function y=x3−3x, plot the values from the completed table:
Points to plot:
(−3,−18)
(−2,−2)
(−1,2)
(0,0)
(1,−2)
(2,2)
(3,18)
After plotting these points on the coordinate axes, connect them smoothly to form the curve. Ensure the curve shows the characteristic shape of a cubic function and passes through all the points plotted.
Step 3
Use your graph to solve $x^3 - 3x = 10$
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Answer
To solve the equation x3−3x=10, we can rearrange it as y=x3−3x and find where the graph intersects the line y=10.
Draw a horizontal line at y=10 on the graph.
Identify the points where the graph of y=x3−3x intersects the line.
These intersection points will provide the solutions to the equation.
From the graph, it's likely that there will be one or more points (likely around xextvalues>2 based on the shape of the cubic function). Approximate the intersection points to find the solutions.
