Find the domain and range of the function
\[ y = \sqrt{-x^2 - 6x + 2} \]
Answer (2)
"> y = − x 2 − 6 x + 2 D : − x 2 − 6 x + 2 ≥ 0 a = − 1 ; b = − 6 ; c = 2 Δ = b 2 − 4 a c ; i ff Δ ≥ 0 t h e n x 1 = 2 a − b − Δ ; x 2 = 2 a − b + Δ Δ = ( − 6 ) 2 − 4 ⋅ ( − 1 ) ⋅ 2 = 36 + 8 = 44 ; Δ = 44 = 4 ⋅ 11 = 2 11 x 1 = 2 ⋅ ( − 1 ) 6 − 2 11 = − 3 + 11 ; x 2 = 2 ⋅ ( − 1 ) 6 + 2 11 = − 3 − 11 l oo k a t t h e p i c t u re D : x ∈ ⟨ − 3 − 11 ; − 3 + 11 ⟩
The domain of the function y = − x 2 − 6 x + 2 is D : [ − 3 − 11 , − 3 + 11 ] and the range is R : [ 0 , 29 ] .
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