Question

Find the equation of the quadratic function that passes through the
points (1,2), (3,-4), and (7,12).

Answer 1

Answer:

$y = \frac{7}{6} x^{2} - 7\frac{2}{3} x + \frac{17}{2}$

Step-by-step explanation:

$y = ax^{2} + bx + c\\2 = a + b + c\\-4 = 9a + 3b + c\\12 = 49a + 7b + c$

Let's eliminate the c.  Take the second and subtract the first.  Take the third and subtract the first.

$-6 = 8a+2b\\10=48a+6b$

Now take 3 times the first and subtract from the second.

$28 = 24a\\a = \frac{7}{6}$

Substitute back to calculate b.

$b=-7\frac{2}{3}$

Substitute back to calculate c.

$c=\frac{17}{2}$