Answer:
[tex]y=2(x+6)^2+7[/tex]
[tex](-6,7)[/tex]
Step-by-step explanation:
[tex]y=2x^2+24x+79[/tex]
Completing the square is a process of converting a quadratic equation in standard form into vertex form.
The first step in completing the square is grouping the quadratic and linear terms of the quadratic equation.
[tex]y=(2x^2+24x)+79[/tex]
Factor out the coefficient of the quadratic term,
[tex]y=2(x^2+12x)+79[/tex]
Now complete the square, add a term to make the grouped part of the equation a complete square, then balance the equation.
[tex]y=2(x^2+12x+36-36)+79[/tex]
Simplify,
[tex]y=2(x^2+12x+36)+79+(2)(-36)[/tex]
[tex]y=2(x+6)^2+79-72[/tex]
[tex]y=2(x+6)^2+7[/tex]
The x-coordinate of the vertex of the equation is equal to (-1) times the numerical part of the quadratic term, and the y-coordinate is equal to the constant.
[tex](-6,7)[/tex]
