Given the equation:

\[ y = -2x^2 - 12x - 23 \]

Find the vertex of the parabola.

y = − 2 x 2 − 12 x − 23 a = − 2 , b = 12 , c = − 23 v er t e x ( h , k ) i s g i v e n b y : h = 2 a − b ​ , k = 4 a − Δ ​
Δ = b 2 − 4 a c = 1 2 2 − 4 ⋅ ( − 2 ) ⋅ ( − 23 ) = 144 − 184 = − 40
h = 2 ⋅ ( − 2 ) 12 ​ = − 4 12 ​ = − 3 k = 4 ⋅ ( − 2 ) 40 ​ = − 8 40 ​ = − 5 A n s w er : v er t e x ( − 3 , − 5 )

Answered by Lilith | 2024-06-10

-b / 2a = 12 / -4 = -3; -Δ / 4a = - ( 144 - 184 ) / -8 = 40 / -8 = -5

Answered by crisforp | 2024-06-10

The vertex of the parabola given by the equation y = − 2 x 2 − 12 x − 23 is ( − 3 , − 5 ) . This was found by using the vertex formula and substituting values into the quadratic equation. The x-coordinate was calculated as − 3 and the y-coordinate as − 5 .
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Answered by Lilith | 2024-12-26