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

How To Solve Use Completing The Square To Find The Vertex Of The Following Parabolas class=

Sagot :

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

[tex]g(x)=x^2-5x+14[/tex]

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

[tex]g(x)=x^2-5x+(\frac{5}{2})^2-(\frac{5}{2})^2+14[/tex]

- simplify the expression as follows:

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

From the general vertex equation, given as:

[tex]g(x)=a(x-h)^2+k[/tex]

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

Therefore, given:

[tex]g(x)=(x^{}-\frac{5}{2})^2+\frac{31}{4}^{}[/tex]

We have the vertex to be:

[tex](\frac{5}{2},\frac{31}{4})\text{ or (2.5, 7.75)}[/tex]

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