Answer:
Vertically stretch by a factor of 2 and vertically shift down by 7 units.
The equation for this parabola is : [tex]y =2x^2- 7[/tex]
Step-by-step explanation:
A equation of parabola is: [tex]y =x^2[/tex]
To do the transformation which includes a vertical stretch and a vertical shift.
Vertical stretch means when you multiply a function by a positive value k,
then you will be performing either a vertical compression or vertical stretching of the graph.
if 0<k<1 , then the graph have a vertical compression and
if k> 1 then the graph have a vertical stretching.
Vertical shift states that for a function f(x) , a new function g(x) = f(x) + c where c is constant is a vertical shift of the function f(x).
If c is positive, the graph will shift up and
if k is negative, the graph will shift down.
From the figure,
we can say that the graph is vertically shift 7 units down
and the graph is vertically stretch by a factor of 2.
Therefore, the equation for the parabola shown in graph is :
[tex]y =2x^2- 7[/tex]
