How do you find the axis of symmetry, and the maximum or minimum value of the function #f(x)=-4(x+1)^2+1#?

Answer 1

See below.

The axis of symmetry of a parabola occurs at its vertex, and if the parabola is not rotated, it is just the vertical line through the vertex.

The vertex is #(-1,1)#, so the axis of symmetry is #x=-1#.
A parabola has a minimum if #a# is positive in #y=a(x-h)^2+k#, and a maximum if #a# is negative. In this case, #a=-4#, so there will be a maximum.
The maximum also occurs at the vertex, so the maximum value of this graph is #1# (the #y#-coordinate value)
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Answer 2

To find the axis of symmetry of the function ( f(x) = -4(x+1)^2 + 1 ), you use the formula for the axis of symmetry, which is ( x = -\frac{b}{2a} ) for a quadratic function in the form ( f(x) = ax^2 + bx + c ). In this case, the coefficient of ( x^2 ) is ( a = -4 ) and the coefficient of ( x ) is ( b = 0 ).

To find the maximum or minimum value of the function, you evaluate the function at the ( x )-coordinate of the axis of symmetry. Then, substitute the value of the axis of symmetry into the function to find the corresponding ( y )-coordinate.

Therefore, the axis of symmetry is ( x = -\frac{0}{2*(-4)} = 0 ).

To find the maximum or minimum value, substitute ( x = 0 ) into the function: [ f(0) = -4(0+1)^2 + 1 = -4(1)^2 + 1 = -4(1) + 1 = -4 + 1 = -3 ]

So, the maximum or minimum value of the function is ( y = -3 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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