Find the vertex and x-intercepts of the function:
\[ y = -x^2 - 6x - 5 \]
Answer (2)
y = − x 2 − 6 x − 5 \tstandard f or m y = a x + b x + c V ( p , q ) p = 2 a − b = − 2 − ( − 6 ) = 3 Δ = b 2 − 4 a c = 1 4 2 − 4 ∗ 1 ∗ ( − 51 ) = 196 + 204 = 400 q = 4 a − Δ = 4 − 400 = 100 V ( 3 , 100 ) x 1 = 2 a − b − Δ = 2 − 14 − 400 = 2 − 14 − 20 = 2 − 34 = − 17 x 2 = 2 a − b + Δ = 2 − 14 + 400 = 2 − 14 + 20 = 2 6 = 3
The vertex of the function y = − x 2 − 6 x − 5 is at V ( − 3 , 4 ) . The x-intercepts of the function are ( − 1 , 0 ) and ( − 5 , 0 ) .
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