Write in vertex form by completing the square:
\[ y = 4x^2 + 40x + 96 \]
Answer (2)
y = 4 x 2 + 40 x + 96 T h e v er t e x f or m o f t h e f u n c t i o n i s : y = a ( x − h ) 2 + k v er t e x = ( h , k ) i s g i v e n b y : h = 2 a − b , k = c − 4 a b 2 a = 4 , b = 40 , c = 96
h = 2 ⋅ 4 − 40 = 8 − 40 = − 5 k = 96 − 4 ⋅ 4 4 0 2 = 96 − 16 1600 = 96 − 100 = − 4 y = 4 ( x − ( − 5 ) ) 2 + ( − 5 ) = 4 ( x + 5 ) 2 − 5
The quadratic equation y = 4 x 2 + 40 x + 96 can be rewritten in vertex form as y = 4 ( x + 5 ) 2 − 4 . This shows that the vertex of the parabola is at the coordinates ( − 5 , − 4 ) .
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