If $(- 3, 10), (0, 1)$ and $(2, 15)$ lies on $y = a x^{2} + b x + c$ , the what is the value of $a + b + c$ ?

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Solution

$y = a x^{2} + b x + c$
Substituting the given co-ordinates to form 3 different equations we get,
$10 = 9 a - 3 b + c$ ...(1)
$1 = c$ ...(2)
$15 = 4 a + 2 b + c$ ...(3)
Substituting eq. (2) in eq.(1) and eq(3), we get
$3 = 3 a - b$ ...(4)
$7 = 2 a + b$ ...(5)
Adding eq(4) and eq(5), we get
$10 = 5 a$
$\Rightarrow a = 2$ and $b = 3$
So, $a + b + c = 2 + 3 + 1 = 6$

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