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Please help me with this
thanks and plz explain
plz help

Please help me with this thanks and plz explain plz help-example-1

1 Answer

3 votes
You're looking to put this into vertex form, which is:


\sf y=a(x-h)^2+k

Where
\sf (h,k) is the vertex of the parabola(minimum).

You currently have it in standard form, which is:


\sf y=ax^2+bx+c

To go from standard form to vertex form, we need to complete the square. But first, let's factor out the coefficient of the first term out of the first two terms:


\sf p^2-28p+250


\sf 1(p^2-28p)+250

Now let's complete the square inside of the parenthesis. We take half of the second term(-28p), square it, and then add it and subtract it into the parenthesis(because we have to keep the function the same). Half of -28 is -14, -14 squared is 196:


\sf 1(p^2-28p+196-196)+250

Now the first three terms in the parenthesis are a perfect square, we can factor them:


\sf 1((p-14)^2-196)+250

Distribute 1 into the parenthesis(anything times 1 is itself):


\sf (p-14)^2-196+250

Combine like terms:


\boxed{\sf (p-14)^2+54}
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