Question

How to solve Use completing the square to find the vertex of the following parabolas

Answer 1

To use completing the square to find the vertex of the given parabola, we proceed as follows:

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

- we divide the coefficient of x by 2 and add and subtract the square of the result, as follows:

`g(x)=x^2-5x+((5)/(2))^2-((5)/(2))^2+14`

- simplify the expression as follows:

`\begin{gathered} g(x)=(x^2-5x+((5)/(2))^2)-((5)/(2))^2+14 \\ \end{gathered}`
`g(x)=(x^{}-(5)/(2))^2-((5)/(2))^2+14`
`g(x)=(x^{}-(5)/(2))^2-(25)/(4)^{}+14`
`g(x)=(x^{}-(5)/(2))^2-(25)/(4)^{}+(56)/(4)`
`g(x)=(x^{}-(5)/(2))^2+(-25+56)/(4)^{}`
`g(x)=(x^{}-(5)/(2))^2+(31)/(4)^{}`

From the general vertex equation, given as:

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

The coordinate of the vertex is taken as: (h, k)

Therefore, given:

`g(x)=(x^{}-(5)/(2))^2+(31)/(4)^{}`

We have the vertex to be:

`((5)/(2),(31)/(4))\text{ or (2.5, 7.75)}`