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Giải bài tập 3 trang 10 SGK Toán 9 tập 2 - Chân trời sáng tạo

Cho hai hàm số (y = frac{1}{4}{x^2})và (y = - frac{1}{4}{x^2}). Vẽ đồ thị của hai hàm số đã cho trên cùng một mặt phẳng tọa độ Oxy.

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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Đề bài

Cho hai hàm số \(y = \frac{1}{4}{x^2}\)và \(y =  - \frac{1}{4}{x^2}\). Vẽ đồ thị của hai hàm số đã cho trên cùng một mặt phẳng tọa độ Oxy.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Để vẽ đồ thị hàm số \(y = a{x^2}\left( {a \ne 0} \right)\), ta thực hiện các bước sau: + Lập bảng giá trị của hàm số với một số giá trị của x (thường lấy 5 giá trị gồm số 0 và hai cặp giá trị đối nhau). + Trên mặt phẳng tọa độ Oxy, đánh dấu các điểm (x;y) trong bảng giá trị (gồm điểm (0;0) và hai cặp điểm đối xứng nhau qua trục Oy). + Vẽ đường parabol đi qua các điểm vừa được đánh dấu.

Lời giải chi tiết

Bảng giá trị của hàm số:

Trên mặt phẳng tọa độ, lấy các điểm A(-4;4), B(-2; 1), O(0;0), C(2; 1), D(4;4) A’(-4;-4), B’(-2; -1), C’(2; -1), D’(4;-4) Đồ thị hàm số \(y = \frac{1}{4}{x^2}\)là một đường parabol đỉnh O, đi qua các điểm A(-4;4), B(-2; 1), O(0;0), C(2; 1), D(4;4) và có dạng như dưới. Đồ thị hàm số \(y =  - \frac{1}{4}{x^2}\)là một đường parabol đỉnh O, đi qua các điểm A’(-4;-4), B’(-2; -1), O(0;0), C’(2; -1), D’(4;-4) và có dạng như dưới.

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