completing the square a>1

​Complete the Square a>1

​Convert y=ax²+bx+c to y=a(x-h)²+k

The first step is factoring out 'a' from the first two terms.

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Don't factor 'a' out of the constant term because that becomes k.​

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Completing the Square to write in vertex form.

​Factor a out of ax²+bx, not c

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.

​Keeping the balance

Completing the Square to write in vertex form.

​Simplify

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​

​Find p, the focus & 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​

​Solve for roots (x-intercepts)

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​