# How do you find the axis of symmetry, and the maximum or minimum value of the function #y = x^2 + 4x + 4#?

The axis of symmetry is x = -2

The minimum of the function is 0

Now that we have the x value, we can plug this in to find the y value, which will always be either a max or a min for the axis of symmetry.

We find that y = 0.

Therefore 0 is the minimum value. The axis of symmetry is x = -2

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To find the axis of symmetry of the function (y = x^2 + 4x + 4), use the formula:

[x = -\frac{b}{2a}]

where (a) is the coefficient of (x^2) (which is (1)) and (b) is the coefficient of (x) (which is (4)).

Substituting the values into the formula, we get:

[x = -\frac{4}{2 \times 1} = -2]

So, the axis of symmetry is (x = -2).

To find the maximum or minimum value of the function, since the coefficient of (x^2) is positive, the parabola opens upwards, indicating that the function has a minimum value.

To find this minimum value, substitute (x = -2) into the function:

[y = (-2)^2 + 4(-2) + 4 = 4 - 8 + 4 = 0]

So, the minimum value of the function is (y = 0).

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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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