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.

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

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

$y=\frac{3}{4}(x-4)^2-2$

The image below shows the parabola.

The function would be

$f(x)=\frac{3}{4}(x-4)^2-2$