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{:[y=-x^(2)-6x-3],[x=-(b)/(2a)]:}

y=−x2−6x−3x=−b2a \begin{array}{l}y=-x^{2}-6 x-3 \\ x=-\frac{b}{2 a}\end{array}

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Full solution

Q. y=−x2−6x−3x=−b2a \begin{array}{l}y=-x^{2}-6 x-3 \\ x=-\frac{b}{2 a}\end{array}
  1. Identify Quadratic Equation: Identify the quadratic equation in the form y=ax2+bx+cy = ax^2 + bx + c. Here, a=−1a = -1, b=−6b = -6, and c=−3c = -3.
  2. Calculate Vertex x-coordinate: Use the formula for the x-coordinate of the vertex, x=−b2ax = -\frac{b}{2a}. Plug in the values of aa and bb. x=−−62⋅(−1)x = -\frac{-6}{2\cdot(-1)}
  3. Simplify xx Calculation: Simplify the calculation for xx.x=6(−2)x = \frac{6}{(-2)}x=−3x = -3
  4. Find Vertex y-coordinate: Now, find the y-coordinate of the vertex by plugging x=−3x = -3 into the original equation.y=−(−3)2−6∗(−3)−3y = -(-3)^2 - 6*(-3) - 3
  5. Simplify y Calculation: Simplify the calculation for y.\newliney = −(9)+18−3-(9) + 18 - 3\newliney = −9+18−3-9 + 18 - 3\newliney = 66

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