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What is the axis of symmetry and vertex for the graph #y= -x^2 + 1#?

Answer 1

Isaiah Anthony

Axis of symmetry is #x=0# (#y#-axis) and vertex is #(0,1)#

The axis of symmetry of #(y-k)=a(x-h)^2# is #x-h=0# and vertex is #(h,k)#.

As #y=-x^2+1# can be written as

#(y-1)=-1(x-0)^2#

hence axis of symmetry is #x-0=0# i.e. #x=0# (#y#-axis) and vertex is #(0,1)#

graph{-x^2+1 [-10.29, 9.71, -6.44, 3.56]}

Note: The axis of symmetry of #(x-h)=a(y-k)^2# is #y-k=0# and vertex is #(h,k)#.

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Answer 2

Eva Abramson

Axis of symmetry: The axis of symmetry for the graph of the quadratic function (y = -x^2 + 1) is the vertical line that passes through the vertex of the parabola.

To find the axis of symmetry, we use the formula (x = -\frac{b}{2a}) from the vertex form of a quadratic function (y = a(x - h)^2 + k), where ((h, k)) is the vertex.

In the equation (y = -x^2 + 1), (a = -1), (b = 0), and (c = 1). Substituting these values into the formula, we get:

[x = -\frac{0}{2(-1)} = 0]

So, the axis of symmetry is (x = 0).

Vertex: To find the vertex, we substitute (x = 0) into the equation:

[y = - (0)^2 + 1 = 1]

Therefore, the vertex of the parabola is at the point ((0, 1)).

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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.