# Question #2e63a

Jun 24, 2016

Referring to the same frame, the second $y = {x}^{2}$ graph is the parabola with vertex at O, axis along y-axis and focus at $\left(0 , \frac{1}{4}\right)$. The 1st $y = {x}^{2} - 3$ graph is this brought down, by 3 units,

#### Explanation:

Referring to the same frame of axes, for both the graphs, the second

$y = {x}^{2}$ graph is the parabola with vertex at O, axis along y-axis

and focus at $\left(0 , \frac{1}{4}\right)$. The graph for the first parabola $y = {x}^{2} - 3$ is

obtained by moving the second down, by 3 units,

The parabolas are of the same size $a = \frac{1}{4}$. They are coaxial,

along y-axis, upwards..

The vertex of the first $y + 3 = {x}^{2}$ is at $\left(0 , - 3\right)$ and its focus is at
$\left(0 , - \frac{11}{4}\right)$.