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 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 $y = 2x + 2$
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To solve the equation x2−2x−2=0, we first rearrange it into the form y=x2−2x−2. We can identify the corresponding linear function to graph alongside the quadratic, which is y=0 for the x-intercepts.
Step 2
Identify points of intersection
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
From the graph of the quadratic, we find points where the graph intersects the line y=0. The estimated intersection points appear to be around xhickapprox−1 and xhickapprox3.
Step 3
Verify the estimated values
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To confirm, we check the values in the range of x. The function x2−2x−2 has approximate roots in the vicinity of −1 and 3. These can be visually verified on the graph to lie close to the x-axis.
Step 4
Provide final solutions
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Thus, the estimated solutions for the equation x2−2x−2=0 are approximately x=−1 and x=3.
