# How do you solve y=x^2+3?

May 18, 2018

As such, you can not 'solve' this

#### Explanation:

Consider the parent graph of $y = {x}^{2}$ This is of general shape $\cup$ and the bottom of the curved part (vertex) ist at the origin $\left(x , y\right) \to \left(0 , 0\right)$

Now if we add 3 we are effectively 'lifting' the whole thing up by 3. So now the vertex is still on the on the y-axis but at the point $\left(x , y\right) \to \left(0 , 3\right)$ instead of $\left(0 , 0\right)$

Mathematically:

The graph crosses the y-axis at $x = 0$ so by substitution:

$y = {x}^{2} + 3 \textcolor{w h i t e}{\text{dddd")-> color(white)("dddd}} y = {\left(0\right)}^{2} + 3 = 3$