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

##### 1 Answer
Jan 30, 2016

${\left(x , y\right)}_{\text{minimum}} = \left(1 , 2\right)$

axis of symmetry $\to x = 1$

#### 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 ${\left(x - 1\right)}^{2}$

Multiply this by negative 1 giving $\left(- 1\right) \times \left(- 1\right) = + 1$

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 ${\left(x , y\right)}_{\text{minimum}} = \left(1 , 2\right)$