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Two parabolas graphed in the xy plane have the equations y=2(x-3)^(2)-7 and y=-(x+a)^(2)+2, where a is a constant. For what value of a will the two parabolas have the same axis of symmetry? Choose 1 answer: (A) 3 (B) -3 (c) 6 (D) -6

Two parabolas graphed in the xy x y plane have the equations y=2(x−3)2−7 y=2(x-3)^{2}-7 and y=−(x+a)2+2 y=-(x+a)^{2}+2 , 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) 33\newline(B) −3-3\newline(C) 66\newline(D) −6-6

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Q. Two parabolas graphed in the xy x y plane have the equations y=2(x−3)2−7 y=2(x-3)^{2}-7 and y=−(x+a)2+2 y=-(x+a)^{2}+2 , 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) 33\newline(B) −3-3\newline(C) 66\newline(D) −6-6
  1. Finding the axis of symmetry for the first parabola: 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. Let's find the axis of symmetry for the first parabola.\newlineThe first parabola is given by y=2(x−3)2−7y = 2(x - 3)^2 - 7.\newlineThe axis of symmetry for this parabola is x=3x = 3.
  2. Finding the axis of symmetry for the second parabola: Now let's find the axis of symmetry for the second parabola.\newlineThe second parabola is given by y=−(x+a)2+2y = -(x + a)^2 + 2.\newlineThe axis of symmetry for this parabola is x=−ax = -a.
  3. Setting the values of h equal: For the two parabolas to have the same axis of symmetry, the values of h from both equations must be equal.\newlineSo we set 33 equal to -a.\newline33 = -a
  4. Solving for aa: Solving for aa, we get:\newlinea=−3a = -3

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