Question

How do you find the axis of symmetry, graph and find the maximum or minimum value of the function `y = (x - 1)^2 + 2`?

Answer 1

`(x,y)_("minimum")= (1,2)`

axis of symmetry `-> x=1`

Explanation:

This is a quadratic equation that has been changed such that it is in vertex form. You virtually read the values you are asked to find almost directly from this.

Consider the -1 from `(x-1)^2`

Multiply this by negative 1 giving `(-1)xx(-1)=+1`

So the axis of symmetry is the line parallel to the y-axis defined by # x=1#

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As `x^2` is positive it means the general shape of the quadratic is like the letter U. So we have a minimum.

We already have the value of x all we need now is the value for y.

As it happens this is the value of the constant in the equation

So `(x,y)_("minimum")= (1,2)`