# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y=(x+1)^2 - 4?

May 8, 2018

Axis of symmetry: $x = - 1 \forall y$
Graph parabola
${y}_{\min} = - 4$

#### Explanation:

$y = {\left(x + 1\right)}^{2} - 4$

$= {x}^{2} + 2 x - 3$

$y$ is a quadratic function of the form $a {x}^{2} + b x + c$ which will have a parabolic graph.

The axis of symmetry will occur where $x = - \frac{b}{2 a}$

$\therefore x = - \frac{2}{2 \times 1} = - 1$

Hence, the axis of symmetry is the vertical line $x = - 1 \forall y$

Since $a > 0 , y$ will have a minimum value on the axis of symmetry.

Thus, ${y}_{\min} = {\left(- 1\right)}^{2} + 2 \left(- 1\right) - 3$

$= 1 - 2 - 3 = - 4$

The graph of $y$ is shown below.

graph{(x+1)^2-4 [-6.406, 6.08, -4.64, 1.6]}