Question

I don’t know what I’m doing but evaluate if f(1)

Answer 1

11

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.