# What is the axis of symmetry and vertex for the graph y=x^2?

May 23, 2016

See the explanation

#### Explanation:

Consider the standard equation of $y = a {x}^{2} + b x + c$

If $a$ is positive then the graph is of shape $\cup$

If $a$ is negative then the graph is of shape $\cap$

$\textcolor{b l u e}{\text{In your equation "a=+1" so the graph is of shape } \cup}$

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The $b x$ term moves the graph left or right from the y axis.

In your equation $b = 0$ ( there is no $b x$ term)

$\textcolor{b l u e}{\text{In your graph axis of symmetry is the y axis}}$
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The constant of $c$ is the y intercept.

In your equation $c = 0$ so the y-intercept is the vertex as the axis of symmetry is the y axis

$\textcolor{b l u e}{\text{In your equation the vertex } \to \left(x , y\right) \to \left(0 , 0\right)}$