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Two parabolas graphed in the xy plane have the equations y=2(x-4)^(2)+2 and y=-(x-a)^(2)+12, where a is a constant. For what value of a will the two parabolas have the same axis of symmetry? Choose 1 answer: (A) 4 (B) -4 (c) 8 (D) -8

Two parabolas graphed in the xy x y plane have the equations y=2(x−4)2+2 y=2(x-4)^{2}+2 and y=−(x−a)2+12 y=-(x-a)^{2}+12 , where a a is a constant. For what value of a a will the two parabolas have the same axis of symmetry?\newlineChoose 11 answer:\newline(A) 44\newline(B) −4-4\newline(C) 88\newline(D) −8-8

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Q. Two parabolas graphed in the xy x y plane have the equations y=2(x−4)2+2 y=2(x-4)^{2}+2 and y=−(x−a)2+12 y=-(x-a)^{2}+12 , where a a is a constant. For what value of a a will the two parabolas have the same axis of symmetry?\newlineChoose 11 answer:\newline(A) 44\newline(B) −4-4\newline(C) 88\newline(D) −8-8
  1. Axis of Symmetry for Parabola 11: The axis of symmetry for a parabola in the form y=A(x−h)2+ky = A(x - h)^2 + k is the vertical line x=hx = h. For the first parabola, y=2(x−4)2+2y = 2(x - 4)^2 + 2, the axis of symmetry is x=4x = 4.
  2. Axis of Symmetry for Parabola 22: For the second parabola, y=−(x−a)2+12y = -(x - a)^2 + 12, the axis of symmetry is x=ax = a.
  3. Setting Axes Equal: Since we want the two parabolas to have the same axis of symmetry, we set their axes equal to each other: 4=a4 = a.
  4. Solving for aa: Solving for aa, we find that a=4a = 4.

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