The equation of a parabola is y=x2+6x+9. Write the equation in vertex form. Simplify any fractions.

Step-by-step explanation:

Vertex form is accomplished by completing the square on the quadratic. Do this by first setting the parabola equal to 0 then moving the constant over to the other side:

Now take half the linear term, square it, and add it to both sides. Our linear term is 6. Half of 6 is 3, and 3 squared is 9:

The reason we do this is to create a perfect square binomial on the left:

(obviously the 0 results from the addition of 9 and -9). Move the 0 back over to the other side and set the quadratic back equal to y:

This gives you a vertex of (-3, 0), which is a minimum value, since the parabola opens upwards.

it would open into a square depending on the type of envelope i’m not sure about the second part

explanation:

remove parenthesis:

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apply rule

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multiply fractions:

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divide:

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mordancy.