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svet-max [94.6K]
3 years ago
8

Find the equation of the quadratic function that passes through the

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
5 0

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}

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