How do you graph and label the vertex and axis of symmetry of #y=(x+4)^2+14#?
Axis of symmetry
Vertex
This is the 'vertex' standard form of the quadratic equation.
Axis of symmetry
Axis of symmetry
Vertex
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To graph the quadratic function ( y = (x+4)^2 + 14 ) and label the vertex and axis of symmetry:

Identify the Vertex: The vertex of the quadratic function in the form ( y = a(x  h)^2 + k ) is ((h, k)). In this equation, ( h = 4 ) and ( k = 14 ), so the vertex is ((4, 14)).

Identify the Axis of Symmetry: The axis of symmetry for a quadratic function in the form ( y = a(x  h)^2 + k ) is the vertical line passing through the vertex, which is ( x = h ). So, the axis of symmetry for this function is ( x = 4 ).

Graphing the Function: Start by plotting the vertex ((4, 14)). Since the coefficient of ( x^2 ) is negative, the parabola will open downwards. Choose additional points on either side of the vertex, such as ( x = 5, 3, 6, 2 ), and evaluate the corresponding ( y ) values using the equation. Plot these points and draw a smooth curve passing through them to form the graph of the function.

Labeling: Label the vertex as ((4, 14)) and draw a dashed vertical line at ( x = 4 ) to represent the axis of symmetry.
That's how you graph and label the vertex and axis of symmetry for the given quadratic function.
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When evaluating a onesided 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 onesided 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 onesided 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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