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Here is the graph of $y = x^2 - 3$ - Edexcel - GCSE Maths - Question 18 - 2019 - Paper 3

Question 18

Here is the graph of $y = x^2 - 3$. Use the graph to find estimates for the solutions to the equation $x^2 - 2x - 2 = 0$. You must show how you get your solution... show full transcript

Worked Solution & Example Answer:Here is the graph of $y = x^2 - 3$ - Edexcel - GCSE Maths - Question 18 - 2019 - Paper 3

Step 1

Identify the equation to solve

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Answer

We need to solve the equation $x^2 - 2x - 2 = 0$ . To do this, we can rewrite it in the form of $y = x^2 - 3$ and relate it to the line $y = 2x + 2$ .

Step 2

Graph the linear equation

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Answer

Using the existing graph of $y = x^2 - 3$ , we add the line $y = 2x + 2$ . This line has a slope of 2 and a y-intercept at (0, 2).

Step 3

Find the intersection points

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Answer

To estimate the solutions, we look for points where the parabola intersects the line $y = 2x + 2$ . We estimate these points to be around $x = -1$ and $x = 3$ .

Step 4

Conclusion

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Answer

The estimated solutions for the equation $x^2 - 2x - 2 = 0$ are approximately $x = -1$ and $x = 3$ .

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