Question

Write equation best represents the graph Please explain in detail how you arrived your answer by staying each mathematical transformation

Answer 1

We are to find the equation of the quadratic curve

By using the vertex method

The equation will be in the form

`y=a(x-h)^2+k`

where, the vertex is at (h, k)

From the graph in the question

The vertex is at (-2, -3)

Therefore,

`h=-2,k=-3`

Therefore the equation of the curve will become

`\begin{gathered} y=a(x-(-2))^2+(-3) \\ y=a(x+2)^2-3 \end{gathered}`

Next, we need to find the value of a

Considering a point on the curve

We have the point (0, 1) on the curve

Hence we have

x = 0, y = 1

Substituting these values in the equation above we have

`\begin{gathered} 1=a(0+2)^2-3 \\ 1=a(2)^2-3 \\ 1+3=4a \\ 4=4a \\ a=(4)/(4) \\ a=1 \end{gathered}`

Therefore, a = 1

Hence the equation of the curve will now become

`\begin{gathered} y=1(x+2)^2-3 \\ y=(x+2)^2-3 \end{gathered}`

Therefore, the answer is

`y=(x+2)^2-3`