Вправи: 411

411. Знайдіть координати вершини параболи.

1) y = x² – 4x;

x₀ = -b2a = 42 = 2; y₀ = ax₀² + bx₀ + c;

y₀ = 4 – 4 • 2 = 4 – 8 = –4; (2; –4).

2) y = x² + 5x;

x₀ = -b2a = -52 = –2,5; y₀ = ax₀² + bx₀ + c;

(–2,5; –6,25).

y₀ = (–2,5)² + 5 • (–2,5) = 6,25 – 12,5 = –6,25.

3) y = –x² + 3;

x₀ = 0, y₀ = –1 • 0 + 3, y₀ = 3; (0; 3).

4) y = 10x² – 5;

x₀ = 0, y₀ = –5, (0; –5).

5) у = х² + 12х – 3; х₀ = -122 = –6;

у₀ = 36 – 12 • 6 – 3 = 36 – 69 = –33; (–6; –33).

6) y = x² + 20x + 30; x₀ = -202 = –10;

y₀ = 100 + 20 • (–10) + 30 = 100 – 200 + 30 = –70;

(–10; –70).

7) y = –6x² – 18x + 1; x₀ = -1812 = –32;

y₀ = –6(–32)² – 18(–32) + 1 = –6 • 94 + 18 • 32 + 1 = –272 + 27 + 1 = -27+227+22 = -27+54+22 = 292 = 14,5; (–32; 14,5).

8) y = 3x² – 24x + 5; x₀ = 246 = 4;

y₀ = 3 • 16 – 24 • 4 + 5 = 48 – 101 = –53; (4; –53).