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vesna_86 [32]
3 years ago
11

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

f its vertex.
Mathematics
1 answer:
katrin2010 [14]3 years ago
7 0

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)

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