Question

Write the function’s equation given this graph. While I know the equation used was the very first one, I’m LT sure how to elaborate or explain

Answer 1

Given: The graph as shown in the image

To Determine: The function of the given image

Solution

Let us determine the vertex of the parabola

The vertex is (-1, -1)

The vertex form of a parabola is

`y=a(x-h)^2+k`
`\begin{gathered} Where \\ vertex=(h,k) \end{gathered}`

Let us substitute the given vertex into the formula

`\begin{gathered} y=a(x-(-1))^2+(-1) \\ y=a(x+1)^2-1 \end{gathered}`
`\begin{gathered} Point(0,0) \\ 0=a(0+1)^2-1 \\ 0=a(1)^2-1 \\ 0=a-1 \\ 1=a \\ a=1 \end{gathered}`

Hence the function is

f(x) = (x + 1)² - 1