Question

The question is: “Write an Equation for each graph. Use the x-y table to check if your equation is correct by plugging in x and y and checking if the statement is true.” My teacher had tried explaining this in the note sheet but her recording messed up and I don’t understand how to do this. Thanks!

Answer 1

From the figure we notice that this graph is a vertical parabola. We know that the equation of a parabola of this kind is

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

where (h,k) is the coordinate of the vertex of the parabola.

From the figure we know that the vertex is the point (2,-3) but we don't know the value of a yet. To find the value of a we notice that the parabola passes through the point (3,-2); this means that in this point x=3 and y=-2.

Using this values in the equation above we have an equation for a.

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

Therefore, the equation of the parabola described in the graph is

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