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first you have to read the graph to see what f(x) is. You know that when x = 0 then y= - 1 so what you have so far is y = ax^2 - 1. You have to guess a bit to see what a is.
Just guessing (and that's all you can do unless you have more information to the question) it looks like when y = 0 then x = about 1.4 or -1.4. That's a good number to have.
y = 1/2 x^2 - 1 is probably the original equation that produced the graph.
So let's check it out.
0 = 1/2 x^2 - 1 Add 1 to both sides.
1 = 1/2 x^2 Multiply by 2
2 = x^2 Take the square root of both sides.
sqrt(2) = sqrt(x^2)
x = +/- sqrt(2)
x = +/- 1.4142 about. So our graph is a pretty good approximation of y = (1/2)x^2 - 1
Now what you want is f(x).
y and f(x) are very close to being equal so we have f(x) = 1/2 x^2 - 1
Now you can solve for f(1)
f(1) = 1/2 (1)^2 - 1
f(1) = 1/2 (1) - 1
f(1) = 1/2 - 1
f(1) = - 1/2 <<<<< Answer.
