Answer:
[tex]y = \frac{7}{6} x^{2} - 7\frac{2}{3} x + \frac{17}{2}[/tex]
Step-by-step explanation:
[tex]y = ax^{2} + bx + c\\2 = a + b + c\\-4 = 9a + 3b + c\\12 = 49a + 7b + c\\[/tex]
Let's eliminate the c. Take the second and subtract the first. Take the third and subtract the first.
[tex]-6 = 8a+2b\\10=48a+6b\\[/tex]
Now take 3 times the first and subtract from the second.
[tex]28 = 24a\\a = \frac{7}{6}[/tex]
Substitute back to calculate b.
[tex]b=-7\frac{2}{3}[/tex]
Substitute back to calculate c.
[tex]c=\frac{17}{2}[/tex]
