Question

Write a quadratic function whose graph passes through (2,1) and has the vertex (4,-2) y=

Answer 1

The given point is (2,1), and the vertex is (4, -2). This means h = 4, and k = -2.

To find the equation, we have to find the parameter a with the given information and the vertex form.

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

Let's replace the given point and the vertex.

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

Now, we replace the parameter a and the vertex to find the equation of the parabola.

`y=(3)/(4)(x-4)^2-2`

The image below shows the parabola.

The function would be

`f(x)=(3)/(4)(x-4)^2-2`