Question

The graph of a function f is shown below.
Find f (0).
W

Answer 1

The function
`\( f(x) = x^2 - 2 \)` describes a parabola with its vertex at
`\((0, -2)\)`. Thus,
`\( f(0) = -2 \)`.

The general form of a parabola that is symmetric about the y-axis is given by:

`\[ f(x) = a x^2 + b x + c \]`

Since the vertex is at y = -2, we know that c = -2. Additionally, since the parabola touches the x-axis at -2 and 2, these are the roots of the equation. Therefore, we can write:

`\[ (x + 2)(x - 2) = 0 \]`

Expanding and setting this equation to zero gives us:

`\[ x^2 - 4 = 0 \]`

So, the coefficient a is 1. The function f(x) is then:

`\[ f(x) = x^2 - 2 \]`

Now, to find f(0), we substitute x = 0 into the function:

`\[ f(0) = 0^2 - 2 = -2 \]`

Therefore, f(0) = -2.