Convert to vertex form:

\[ y = 2x^2 + 14x - 4 \]

T o co n v er t t h e s t an d a r d f or m y = a x 2 + b x + c o f a f u n c t i o n in t o v er t e x f or m y = a ( x − h ) 2 + k Here t h e p o in t ( h , k ) i s c a ll e d a s v er t e x h = 2 a − b ​ , k = c − 4 a b 2 ​
y = 2 x 2 + 14 x − 4 a = 2 , b = 14 , c = − 4 h = 2 ∗ 2 − 14 ​ = − 4 14 ​ = − 3.5 k = − 4 − 4 ⋅ 2 1 4 2 ​ = − 4 − 8 196 ​ = − 4 − 24.5 = − 28.5 y = 2 ( x + 3.5 ) 2 − 28.5

Answered by Lilith | 2024-06-10

y = 2 x 2 + 14 x − 4 a = 2 ; b = 14 ; c = − 4 v er t e x f or m : y = a ( x − h ) 2 + k w h ere : h = 2 a − b ​ an d k = 4 a − ( b 2 − 4 a c ) ​ h = − 2 ⋅ 2 − 14 ​ = − 2 7 ​ k = 4 ⋅ 2 − ( 1 4 2 − 4 ⋅ 2 ⋅ ( − 4 )) ​ = 8 − ( 196 + 32 ) ​ = 8 − 228 ​ = − 2 57 ​ A n s w er : y = 2 ( x + 2 7 ​ ) 2 − 2 57 ​

Answered by Anonymous | 2024-06-10

The quadratic equation y = 2 x 2 + 14 x − 4 can be converted to vertex form as y = 2 ( x + 3.5 ) 2 − 28.5 . This reveals that the vertex of the parabola is located at the point (-3.5, -28.5).
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Answered by Lilith | 2024-12-23