Question

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

Answer 1

axis of symmetry: `color(blue)(x = -4)`
Max: None
Min: `color(blue)((-4, 2)`

Explanation:

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https://www.desmos.com/calculator

To find the axis of symmetry in this equation, you need to understand transformations of functions(KhanAcademy link here).

The easiest way is to graph it but to find it by looking at the function, you have to first find which way the parabola is orientated(in this case, verticle). To find this, find which variable is squared. If it is x, then it is verticle. If it is y, then it is horizontal.

`color(red)"Verticle"`: If the orientation is verticle, then take the vertex's x value and replace it for k in this equation (x = k). This is your axis of symmetry.

`color(green)"Horizontal"`: If the orientation is horizontal, then take the vertex's y value and replace it for h in this equation (y = h). This is the axis of symmetry.

To find the min/max of a verticle parabola, take the opening of the parabola, either up or down(up in this case). If the parabola opens upward, then the vertex is the min. If the parabola opens downward, then the vertex is the max. To find which way the parabola opens, look at the value of a in this equation a(x-k)+h. If it is positive, the parabola opens up. If it is negative, the parabola opens down.

There is not a min/max of a horizontal parabola.