Good evening
Answer:
g(x) = 2x²
Step-by-step explanation:
Here the graph of g passes through the points A(0 , 0) , B(1 , 2) and C(-1 , 2)
and g defined by the equation: y = ax² + bx + c
> the graph of g passes through the points A(0 , 0) Means
0 = 0 + 0 + c then c = 0
> the graph of g passes through the points B(1 , 2) Means
2 = a(1)² + b(1) ⇒ a + b = 2
> the graph of g passes through the points C(-1 , 2) Means
2 = a(-1)² + b(-1) ⇒ a - b = 2
we obtain:
a + b = 2
a - b = 2
after solving this simple system above you will get:
a = 2 and b = 0
finally,
g(x) = 2x²
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