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The functions y=3(x+2)^(2)-4 and y=-3(x+2)^(2)-4 are graphed in the xy-plane. Which of the following must be true of the graphs of the vertexes and axes of symmetry of the two functions? Choose 1 answer: (A) The functions will have different vertexes. (B) The functions will have different axes of symmetry. (C) The function y=3(x+2)^(2)-4 will have a minimum value, and the function y=-3(x+2)^(2)-4 will have a maximum value. (D) The function y=3(x+2)^(2)-4 will have a maximum value, and the graph of y=-3(x+2)^(2)-4 will have a minimum value.

The functions y=3(x+2)2−4 y=3(x+2)^{2}-4 and y=−3(x+2)2−4 y=-3(x+2)^{2}-4 are graphed in the xy x y -plane. Which of the following must be true of the graphs of the vertexes and axes of symmetry of the two functions?\newlineChoose 11 answer:\newline(A) The functions will have different vertexes.\newline(B) The functions will have different axes of symmetry.\newline(C) The function y=3(x+2)2−4 y=3(x+2)^{2}-4 will have a minimum value, and the function y=−3(x+2)2−4 y=-3(x+2)^{2}-4 will have a maximum value.\newline(D) The function y=3(x+2)2−4 y=3(x+2)^{2}-4 will have a maximum value, and the graph of y=−3(x+2)2−4 y=-3(x+2)^{2}-4 will have a minimum value.

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Q. The functions y=3(x+2)2−4 y=3(x+2)^{2}-4 and y=−3(x+2)2−4 y=-3(x+2)^{2}-4 are graphed in the xy x y -plane. Which of the following must be true of the graphs of the vertexes and axes of symmetry of the two functions?\newlineChoose 11 answer:\newline(A) The functions will have different vertexes.\newline(B) The functions will have different axes of symmetry.\newline(C) The function y=3(x+2)2−4 y=3(x+2)^{2}-4 will have a minimum value, and the function y=−3(x+2)2−4 y=-3(x+2)^{2}-4 will have a maximum value.\newline(D) The function y=3(x+2)2−4 y=3(x+2)^{2}-4 will have a maximum value, and the graph of y=−3(x+2)2−4 y=-3(x+2)^{2}-4 will have a minimum value.
  1. Identify Form: Identify the form of the given functions.\newlineBoth functions are in the form of a transformed quadratic function y=a(x−h)2+ky=a(x-h)^2+k, where (h,k)(h, k) is the vertex of the parabola and x=hx=h is the axis of symmetry.
  2. Determine Vertex: Determine the vertex of each function.\newlineFor y=3(x+2)2−4y=3(x+2)^2-4, the vertex is (−2,−4)(-2, -4).\newlineFor y=−3(x+2)2−4y=-3(x+2)^2-4, the vertex is also (−2,−4)(-2, -4).\newlineSince both functions have the same hh and kk values in their vertex form, they share the same vertex.
  3. Axis of Symmetry: Determine the axis of symmetry for each function.\newlineThe axis of symmetry for both functions is x=−2x=-2, as it is derived from the hh value in the vertex (h,k)(h, k).
  4. Parabola Direction: Determine the direction of the parabolas.\newlineThe coefficient of the squared term aa determines the direction of the parabola. If aa is positive, the parabola opens upwards. If aa is negative, the parabola opens downwards.\newlineFor y=3(x+2)2−4y=3(x+2)^2-4, aa is positive, so the parabola opens upwards and has a minimum value.\newlineFor y=−3(x+2)2−4y=-3(x+2)^2-4, aa is negative, so the parabola opens downwards and has a maximum value.

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