Answer
The equation of the red graph is: $$y = x^2+3$$
The equation of the yellow graph is: $$y = x^2-5$$
Work Step by Step
The blue graph is the graph of function $y = x^2$. It collides with the y-axis at point $y = 0$.
1) First, we look at the yellow graph:
- It is a vertical shift. So the equation of the yellow graph has this form:
$$y = x^2+h$$
- The yellow graph shifts to below the blue graph, so $h\lt0$.
- The yellow graph collides with the y-axis at point $y=-5$, which is $5$ units away from the blue graph, so $|h|=5$.
- Since we know that $h\lt0$, we figure that $h=-5$
Therefore, the equation of the yellow graph is: $$y = x^2-5$$
2) Now, about the red graph:
- It is a vertical shift. So the equation of the red graph has this form:
$$y = x^2+h$$
- The red graph shifts to above the blue graph, so $h\gt0$.
- The red graph collides with the y-axis at point $y=3$, which is $3$ units away from the blue graph, so $|h|=3$.
- Since we know that $h\gt0$, we figure that $h=3$
Therefore, the equation of the red graph is: $$y = x^2+3$$
