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

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Question 18

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

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 solutions.

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

Step 1

Find the line $y = 2x + 2$

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Answer

To solve the equation x2−2x−2=0x^2 - 2x - 2 = 0, we first rearrange it into the form y=x2−2x−2y = x^2 - 2x - 2. We can identify the corresponding linear function to graph alongside the quadratic, which is y=0y = 0 for the x-intercepts.

Step 2

Identify points of intersection

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Answer

From the graph of the quadratic, we find points where the graph intersects the line y=0y = 0. The estimated intersection points appear to be around xhickapprox−1x hickapprox -1 and xhickapprox3x hickapprox 3.

Step 3

Verify the estimated values

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Answer

To confirm, we check the values in the range of xx. The function x2−2x−2x^2 - 2x - 2 has approximate roots in the vicinity of −1-1 and 33. These can be visually verified on the graph to lie close to the x-axis.

Step 4

Provide final solutions

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Answer

Thus, the estimated solutions for the equation x2−2x−2=0x^2 - 2x - 2 = 0 are approximately x=−1x = -1 and x=3x = 3.

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