Question

For f(x) = ax^2 + bx + c, if f(1) = 5 and f(-1) = 0, find the value of a + c.

Answer 1

f(x) = ax² + bx + c

f(1) = a(1)² + b(1) + c = 5
f(1) = a + b + c = 5

f(-1) = a(-1)² + b(-1) + c = 0
a - b + c = 0

So now we have:
f(1) = a + b + c = 5
f(-1) = a - b + c = 0

We add both the equations up,
f(1) + f(-1) :

2a + 2c = 5
a + c = 2.5 // Divide by 2 through

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Answer: a + c = 2.5
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