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

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