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Giải bài 1 trang 54 vở thực hành Toán 8 tập 2

Cho hai hàm số y = 2x − 1 và y = −x + 2. a) Trong cùng mặt phẳng tọa độ Oxy, vẽ đồ thị của hai hàm số đã cho

𓆏Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Cho hai hàm số y = 2x − 1 và y = −x + 2. a) Trong cùng mặt phẳng tọa độ Oxy, vẽ đồ thị của hai hàm số đã cho b) Tìm tọa độ giao điểm của hai đồ thị trên

Phương pháp giải - Xem chi tiết

a) Xác định hai điểm thuộc đồ thị hàm số y = 2x − 1 và y = −x + 2. Từ đó vẽ trên mặt phẳng tọa độ đồ thị hàm số. b) Xét phương trình hoành độ giao điểm của hai hàm số rồi tìm giao điểm của hàm số.

Lời giải chi tiết

a) Đồ thị của hàm số y = 2x – 1 và y = -x + 2 như hình bên:

b) Gọi A(x0; y0) là giao điểm của hai đường thẳng đã cho. Khi đó, cả hai đường thẳng đã cho đồng thời đi qua điểm A nên ta có: y0 = 2x0 – 1 và y0 = -x0 + 2, suy ra 2x0 – 1 = -x0 + 2, hay x = 1.

Do đó y0 = 1.

Vậy hai đường thẳng đã cho cắt nhau tại điểm A(1; 1).

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