Question

Place the quadratic y=2x^2+24x+79 into vertex form by using the method of completing the square and then state the coordinates of its vertex.

Answer 1

Answer:

$y=2(x+6)^2+7$

$(-6,7)$

Step-by-step explanation:

$y=2x^2+24x+79$

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.

$y=(2x^2+24x)+79$

Factor out the coefficient of the quadratic term,

$y=2(x^2+12x)+79$

Now complete the square, add a term to make the grouped part of the equation a complete square, then balance the equation.

$y=2(x^2+12x+36-36)+79$

Simplify,

$y=2(x^2+12x+36)+79+(2)(-36)$

$y=2(x+6)^2+79-72$

$y=2(x+6)^2+7$

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.

$(-6,7)$