Answer:
The correct answer is [tex]y = \frac{10}{9}(x+3)^2+2[/tex]
Step-by-step explanation:
The correct answer to the question is not provided in the options listed below.
In order to find the equation of the quadratic function that you're looking for, you should identify the two points the parabola passes through: the vertex (that is point (-3,2)) and the y-intercept (the point (0,12)).
As we are given the vertex of the quadratic function, we can use the completed square form: [tex]y=a(x-h)^2+k[/tex], where h and k are, respectively, the x and y coordinates of the vertex.
As (-3,2) is the vertex, we have:
[tex]y=a(x+3)^2+2[/tex]
Now, as the graph passes through the point (0,12), we can replace x=0 and y=12 in the formula above in order to find the value of a. Then, we make a the subject of the equation:
[tex]12=a(0+3)^2+2[/tex]
[tex]12=9a+2[/tex]
[tex] 10=9a[/tex]
[tex] \frac{10}{9}=a[/tex]
So, the equation of the parabola is [tex]y=\frac{10}{9}(x+3)^2+2[/tex].
