completing the square a>1

Sompleting the Square to write in vertex form.

Once x²​ is alone, you can use the new b to add and subtract.

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WARNING - GCF 3 causes problems!​

x²​ must be alone to complete the square. So a must be factored out.

Completing the Square to write in vertex form.

Completing the Square to write in vertex form.

Once we combine the constants, finding the vertex is just (h,k) or​ (opp, same)

Vertex: ( - 4, - 30)​

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We can solve for roots.

We can use 3=1/4p to locate the focus and directrix​

Completing the Square to write in vertex form.

p=1/12

Set 3=1/4p and solve

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​Focus: ( - 4, - 29 11/12)​

Since the parabola opens up the focus is upward. add 1/12 to k​

The directrix is a horizontal line below this parabola.

Subtract from k.​

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y= - 30 1/12​

Completing the Square to write in vertex form.

Move the 30 over and

Divide by 3. ​

Take the square root

(Don't forget ±​)

Subtract 4.​

x≈ - 0.84 and - 7.16​