Find the coordinates of the intersections of y = ax² and the linear function y = bx + c.
📘 Example ①
Find the intersections of y = x² and y = x + 2.
Answer:x² = x + 2 → x² − x − 2 = 0 → (x−2)(x+1) = 0.
x=2 → y=4, x=−1 → y=1. Intersections: (2,4) and (−1,1)
Find the intersections of y = x² and y = x + 2.
Answer:x² = x + 2 → x² − x − 2 = 0 → (x−2)(x+1) = 0.
x=2 → y=4, x=−1 → y=1. Intersections: (2,4) and (−1,1)
💡 Key Point
- Set the two equations equal and solve the quadratic equation
- Once x is found, substitute it into either equation to find y
Practice Problems
- Find the intersections of y = x² and y = 2x + 3.
Answer and Explanation
- Answer:(3,9) and (−1,1). x²=2x+3 → x²−2x−3=0 → (x−3)(x+1)=0.