Question

Use completing the square to find the vertex of the fallen parabolasHow to solve

Answer 1

Given the equation of the parabola:

$g(x)=x^2-5x+14$

We will complete the square to find the vertex

So, we will add and subtract the square of half the coefficient of x

So,

$\begin{gathered} g(x)=x^2-5x+14+(\frac{5}{2})^2-(\frac{5}{2})^2 \\ g(x)=(x^2-5x+(\frac{5}{2})^2)+(14-(\frac{5}{2})^2) \\ g(x)=(x-\frac{5}{2})^2+\frac{31}{4} \\ \\ g(x)=(x-2.5)^2+7.75 \end{gathered}$

So, the answer will be the vertex = (2.5, 7.75)