Question

What is the equation of the graph below?Oy=-(x-3)²-2Oy=-(x + 2)²-3Oy=(x-3)²-2Oy=(x + 2)²-3

Answer 1

Given: The parabola shown

To Determine: The equation of the parabola

Solution

The equation of a parabola given the vertex and a point is given as

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

From the graph, we locate the vertex and the a point A as shown below

So

`\begin{gathered} Vertex=(3,-2) \\ PointA:(4,-1) \end{gathered}`

Substitute the vertex and the point A to get the value of a

`\begin{gathered} y=a(x-h)^2+k \\ -1=a(4-3)^2+(-2) \\ -1=a(1)^2-2 \\ -1=a-2 \\ -1+2=a \\ 1=a \end{gathered}`

Substitute the value of a and the vertex to get the equation of the parabola

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

Hence, the equation of the parabola is

y = (x -3)² - 2