find the standard form of this vertex form of this quadratic function

Question

y=(x+4)^2-16

thank you..with steps please

Answer 1

The standard form of a quadratic equation:
y = a x² + b x + c

in this case:

y = ( x + 4 )² - 16

Apply perfect square formula for ( x + 4 )²
_____________________

( a + b )² = a² + 2 ∙ a ∙ b + b²
_____________________

( x + 4 )² = x² + 2 ∙ x ∙ 4 + 4² = x² + 8 x + 16

Replace ( x + 4 )² = x² + 8 x + 16 in your equation:

y = ( x + 4 )² - 16 = x² + 8 x + 16 - 16

y = x² + 8 x