Asked by Ariana
find the standard form of this vertex form of this quadratic function
y=(x+4)^2-16
thank you..with steps please
y=(x+4)^2-16
thank you..with steps please
Answers
Answered by
Bosnian
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
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
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