ali graphs the function ( f(x)=-(x + 2)^{2}-1 ) as shown. which best describes the error in the graph? the…

ali graphs the function ( f(x)=-(x + 2)^{2}-1 ) as shown. which best describes the error in the graph? the axis of symmetry should be ( x=-1 ). the axis of symmetry should be ( x = 2 ). the vertex should be a maximum. the vertex should be ( (-2,1) ).

ali graphs the function ( f(x)=-(x + 2)^{2}-1 ) as shown. which best describes the error in the graph? the axis of symmetry should be ( x=-1 ). the axis of symmetry should be ( x = 2 ). the vertex should be a maximum. the vertex should be ( (-2,1) ).

Answer

Explanation:

Step1: Recall the vertex form of a parabola

The vertex form of a parabola is (y = a(x - h)^2 + k), where ((h,k)) is the vertex and the axis of symmetry is (x = h). For the function (f(x)=-(x + 2)^2-1), we have (a=-1), (h=-2), and (k = - 1).

Step2: Analyze the direction of the parabola

Since (a=-1<0), the parabola opens downwards. When a parabola opens downwards, the vertex ((h,k)=(-2,-1)) is a maximum point.

Step3: Check each option

  • Option 1: The axis of symmetry for (y=-(x + 2)^2-1) is (x=-2) (not (x = - 1)), so this option is wrong.
  • Option 2: The axis of symmetry for (y=-(x + 2)^2-1) is (x=-2) (not (x = 2)), so this option is wrong.
  • Option 3: Since (a=-1<0), the parabola opens downwards and the vertex ((-2,-1)) is a maximum. This option is correct.
  • Option 4: For (y=-(x + 2)^2-1), (k=-1), so the vertex is ((-2,-1)) (not ((-2,1))), so this option is wrong.

Answer:

The vertex should be a maximum.