Match the graph to the formula. Respond with the number of the formula followed by the letter of the graph, without spaces or commas. For example, if formula 1 matches graph A, the answer is 1A.

Analysis:

• Graph A shows a parabola opening upwards, with its vertex in the first quadrant. The formula for a parabola opening upwards has a positive coefficient for the $$x^2$$ term. Formulas 1 and 2 have a negative coefficient for $$x^2$$, so they represent parabolas opening downwards. Formula 4 has a positive coefficient for $$x^2$$. Let's find the vertex of formula 4: $$y = 2x^2 - 6x + 6$$. The x-coordinate of the vertex is given by $$-b/(2a) = -(-6)/(2*2) = 6/4 = 1.5$$. The y-coordinate is $$2(1.5)^2 - 6(1.5) + 6 = 2(2.25) - 9 + 6 = 4.5 - 9 + 6 = 1.5$$. So the vertex is at (1.5, 1.5). This matches graph A, which has a vertex slightly to the right of 1 and slightly above 1.
• Graph Б shows a parabola opening upwards, with its vertex on the y-axis. This means the x-coordinate of the vertex is 0. Let's examine the formulas for upward-opening parabolas. Formula 4 has vertex (1.5, 1.5). Formula 3 has $$y = 2x^2 + 6x + 6$$. The x-coordinate of the vertex is $$-6/(2*2) = -6/4 = -1.5$$. The y-coordinate is $$2(-1.5)^2 + 6(-1.5) + 6 = 2(2.25) - 9 + 6 = 4.5 - 9 + 6 = 1.5$$. So the vertex is at (-1.5, 1.5). This does not match graph Б. Let's re-examine. The graphs are not precisely to scale, and the labels are 'A', 'Б', 'B'.
• Let's analyze the vertex for each formula:
• 1) $$y = -2x^2 + 6x - 6$$: $$x_v = -6/(2*(-2)) = -6/-4 = 1.5$$. $$y_v = -2(1.5)^2 + 6(1.5) - 6 = -2(2.25) + 9 - 6 = -4.5 + 9 - 6 = -1.5$$. Vertex: (1.5, -1.5). Parabola opens downwards. Matches Graph B.
• 2) $$y = -2x^2 - 6x - 6$$: $$x_v = -(-6)/(2*(-2)) = 6/-4 = -1.5$$. $$y_v = -2(-1.5)^2 - 6(-1.5) - 6 = -2(2.25) + 9 - 6 = -4.5 + 9 - 6 = -1.5$$. Vertex: (-1.5, -1.5). Parabola opens downwards.
• 3) $$y = 2x^2 + 6x + 6$$: $$x_v = -6/(2*2) = -6/4 = -1.5$$. $$y_v = 2(-1.5)^2 + 6(-1.5) + 6 = 2(2.25) - 9 + 6 = 4.5 - 9 + 6 = 1.5$$. Vertex: (-1.5, 1.5). Parabola opens upwards. Matches Graph Б (vertex in the second quadrant, opens upwards).
• 4) $$y = 2x^2 - 6x + 6$$: $$x_v = -(-6)/(2*2) = 6/4 = 1.5$$. $$y_v = 2(1.5)^2 - 6(1.5) + 6 = 2(2.25) - 9 + 6 = 4.5 - 9 + 6 = 1.5$$. Vertex: (1.5, 1.5). Parabola opens upwards. Matches Graph A (vertex in the first quadrant, opens upwards).

Summary of matches:

• Graph A: $$y = 2x^2 - 6x + 6$$ (Formula 4)
• Graph Б: $$y = 2x^2 + 6x + 6$$ (Formula 3)
• Graph B: $$y = -2x^2 + 6x - 6$$ (Formula 1)

The question asks for the answer as a sequence of digits without spaces and commas, in the order indicated. This implies the order of the graphs A, Б, B.

Therefore, the sequence of formula numbers corresponding to graphs A, Б, B is 4, 3, 1.

Ответ: 431