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

Question

Avery Alexander · Accepted Answer

The axis of symmetry is x = -2
The minimum of the function is 0

The formula for the axis of symmetry is given by #x = -b/(2a)# where the quadratic is #y = ax^2 + bx + c#. Therefore just plug the values in: #-4 / 2# => #x =-2# which is the axis of symmetry 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. If a is positive, there will be a min If a is negative, there will be a max (just think back to the parent function #y = x^2# ... it opens upwards with a minimum value) Therefore 0 is the minimum value. The axis of symmetry is x = -2

Eva Adamson · Answer

undefined 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 $y = 0$.