Complete the table for $y = x^2 - 2x$. | $x$ | -1 | 0 | 1 | 2 | 3 | 4 | |-----|----|---|---|---|---|---| | $y$ | 3 | 0 | -1| 0 | 3 | 8 | Draw the graph of $y = x^2 - 2x$ for $-1 \leq x \leq 4$. Use your graph to solve $x^2 - 2x = 2$.

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Complete the table for $y = x^2 - 2x$ - OCR - GCSE Maths - Question 7 - 2017 - Paper 1

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Complete the table for $y = x^2 - 2x$. | $x$ | -1 | 0 | 1 | 2 | 3 | 4 | |-----|----|---|---|---|---|---| | $y$ | 3 | 0 | -1| 0 | 3 | 8 | Draw the graph of $y = x^... show full transcript

Worked Solution & Example Answer:Complete the table for $y = x^2 - 2x$ - OCR - GCSE Maths - Question 7 - 2017 - Paper 1

Step 1

Complete the table for $y = x^2 - 2x$

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Answer

To complete the table, we can substitute the values of $x$ into the equation $y = x^2 - 2x$ :

For $x = -1$ :
$y = (-1)^2 - 2(-1) = 1 + 2 = 3$
For $x = 0$ :
$y = (0)^2 - 2(0) = 0 - 0 = 0$
For $x = 1$ :
$y = (1)^2 - 2(1) = 1 - 2 = -1$
For $x = 2$ :
$y = (2)^2 - 2(2) = 4 - 4 = 0$
For $x = 3$ :
$y = (3)^2 - 2(3) = 9 - 6 = 3$
For $x = 4$ :
$y = (4)^2 - 2(4) = 16 - 8 = 8$

Thus, the completed table becomes:

$x$	-1	0	1	2	3	4
$y$	3	0	-1	0	3	8

Step 2

Draw the graph of $y = x^2 - 2x$ for $-1 \leq x \leq 4$

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Answer

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

The point $(-1, 3)$
The point $(0, 0)$
The point $(1, -1)$
The point $(2, 0)$
The point $(3, 3)$
The point $(4, 8)$

Connect these points smoothly to form a parabolic curve, ensuring that it passes through all defined points for the given range of $x$ .

Step 3

Use your graph to solve $x^2 - 2x = 2$

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Answer

To solve the equation using the graph, rearrange it to the form $y = 0$ :

$x^2 - 2x - 2 = 0$

Now, we need to find the points at which the graph intersects the line $y = 2$ . By observing the graph drawn in part (b), the points of intersection can be identified.

From the graph, it can be determined that the solutions for $x$ are approximately $x \approx 2.9$ and $x \approx -0.9$ . Therefore, the solutions to $x^2 - 2x = 2$ are:

$x \approx 2.9$
$x \approx -0.9$

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Complete the table for $y = x^2 - 2x$ - OCR - GCSE Maths - Question 7 - 2017 - Paper 1

Worked Solution & Example Answer:Complete the table for $y = x^2 - 2x$ - OCR - GCSE Maths - Question 7 - 2017 - Paper 1

Complete the table for $y = x^2 - 2x$

Draw the graph of $y = x^2 - 2x$ for $-1 \leq x \leq 4$

Use your graph to solve $x^2 - 2x = 2$

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