the vertex of a paorabola is y=(x-4)^2+. What is the standard form of the equation?

Question

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Answer 1

Just multiply it out and combine like terms:

 

y = (x-4)² + 22

y = (x-4)(x-4) + 22

 

Can you finish it? Standard form is y = ax² + bx + c.

Answer 2

I am unsure what your textbook takes as the "standard" form.

At least one definition of the standard for with the axis parallel to the y-axis is: (x-h)² = 4p(y-k)

  where the vertex is at (h,k) and focus is at (h,k+p).

In your case apparently h=4, p=1/4 and k=22.

 

Another form which might be referred to as "standard" would be x² -  8x + 38

 

If neither of these is the standard form given in your textbook, please send me a message & I will try to help you further.