Question

Please help me with this
thanks and plz explain
plz help

Answer 1

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}`