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

Apr 11, 2016

$\text{Axis of Symmetry} \to x = - 2$
Minimum at $\left(x , y\right) \to \left(- 2 , - 5\right)$

#### Explanation:

The standard form is $y = a {x}^{2} + b x + c$

$\textcolor{b l u e}{\underline{\text{Determine axis of symmetry and vertex}}}$

This can be written as: $a \left({x}^{2} + \frac{b}{a} x\right) + c \text{ }$ ( in your case a=1)

The axis of symmetry as at $x = \left(- \frac{1}{2}\right) \times \left(\frac{b}{a}\right)$

This is also the value of ${x}_{\text{vertex")-> ("maximum/minimum}}$

color(blue)(x_("vertex")" "=" "(-1/2)xx4=color(red)(-2)" "=" Axis of Symmetry")

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Substitute for $x$ to find ${y}_{\text{vertex}}$

$\textcolor{b l u e}{\implies {y}_{\text{vertex}} = {\left(- 2\right)}^{2} + 4 \left(- 2\right) - 1 = - 5}$

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$\textcolor{b l u e}{\text{So vertex} \to \left(x , y\right) \to \left(- 2 , - 5\right)}$

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$\textcolor{b l u e}{\underline{\text{Determine if maximum or minimum}}}$

The coefficient of ${x}^{2}$ is +1. That is, it is positive. As such the graph is of general shape $\cup$.

color(blue)("Thus the vertex is that of a minimum ")
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