Worked example 1
Find line-curve intersections
Find the intersections of y = x² and y = 2x + 3.
- Set x² = 2x + 3
- Solve x² − 2x − 3 = 0 to get x = −1 or 3.
- Substitute into y = x²
Answer: (-1, 1) and (3, 9).
Higher Mathematics
Higher Maths Intersections of functions
Practise intersections of functions for Scottish Higher Mathematics with worked examples, clear methods and original interactive questions. Find the coordinates where a line and curve, or two curves, have equal outputs.
Before you start
- Solve quadratic equations.
- Substitute x-values into a function.
- Write coordinates in ordered pairs.
Explanation
At an intersection the functions have the same x-input and y-output, so set their expressions equal.
After solving for every x-value, substitute into either original function to obtain the matching y-coordinates.
Method and rules
- At an intersection, f(x) = g(x)
- Each valid x-value needs its own y-value.
- Substitute coordinates back into both equations as a check.
Worked examples
Worked example 2
Method check
How do you begin an intersection question involving y = f(x) and y = g(x)?
- The y-values agree at an intersection.
So: Set f(x) = g(x)
Watch out
- Giving x-values instead of coordinates.
- Missing one quadratic root.
- Using different x-values for the two equations.
Exam reminder
For intersections of functions, show the defining equation or formula before simplifying. Check that every final value satisfies the original restrictions, interval or context.
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