Match the equations to the graphs. A) y=x^2-7x+14, Б) y=x^2+7x+14, B) y=-x^2-7x-14

Matching Graphs to Equations

The graphs represent quadratic functions of the form $$y = ax^2 + bx + c$$. The sign of 'a' determines if the parabola opens upwards (a > 0) or downwards (a < 0). The vertex's position is influenced by 'b' and 'c'.

Graph Analysis:

• Graph A: Opens upwards, vertex in the first quadrant.
• Graph Б: Opens upwards, vertex in the second quadrant.
• Graph B: Opens downwards, vertex in the third quadrant.

Equation Analysis:

• 1) $$y = x^2 - 7x + 14$$: $$a=1$$ (opens up), $$b=-7$$, $$c=14$$. Vertex x-coordinate: $$-b/(2a) = 7/2 = 3.5$$. Vertex y-coordinate: $$(3.5)^2 - 7(3.5) + 14 = 12.25 - 24.5 + 14 = 1.75$$. Vertex (3.5, 1.75) - first quadrant.
• 2) $$y = x^2 + 7x + 14$$: $$a=1$$ (opens up), $$b=7$$, $$c=14$$. Vertex x-coordinate: $$-b/(2a) = -7/2 = -3.5$$. Vertex y-coordinate: $$(-3.5)^2 + 7(-3.5) + 14 = 12.25 - 24.5 + 14 = 1.75$$. Vertex (-3.5, 1.75) - second quadrant.
• 3) $$y = -x^2 - 7x - 14$$: $$a=-1$$ (opens down), $$b=-7$$, $$c=-14$$. Vertex x-coordinate: $$-b/(2a) = 7/(-2) = -3.5$$. Vertex y-coordinate: $$-(-3.5)^2 - 7(-3.5) - 14 = -12.25 + 24.5 - 14 = -1.75$$. Vertex (-3.5, -1.75) - third quadrant.

Matching:

Equation 1 matches Graph A.

Equation 2 matches Graph Б.

Equation 3 matches Graph B.