Problem

$\begin{array}{l}y=a x^{2}+b x+c \\ 2=a(0)^{2}+b(0)+c\end{array}$

Answer

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Answer

\(\boxed{c = 2}\)

Steps

Step 1 :Given the quadratic equation: \(y = ax^2 + bx + c\) and the point \((0, 2)\) on the curve.

Step 2 :Plug in the x and y values from the point into the equation: \(2 = a(0)^2 + b(0) + c\)

Step 3 :Simplify the equation: \(2 = 0 + 0 + c\)

Step 4 :Find the value of c: \(c = 2\)

Step 5 :\(\boxed{c = 2}\)

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