Re-write the quadratic function below in Standard Form \( y=-3(x+4)^{2}+8 \)

Simplify the expression by following steps: - step0: Add the terms: \(-3\left(x+4\right)^{2}+8\) - step1: Expand the expression: \(-3x^{2}-24x-48+8\) - step2: Add the numbers: \(-3x^{2}-24x-40\) To rewrite the quadratic function \( y = -3(x+4)^{2} + 8 \) in standard form, we first expand the expression. 1. Start with the given function: \[ y = -3(x+4)^{2} + 8 \] 2. Expand \( (x+4)^{2} \): \[ (x+4)^{2} = x^{2} + 8x + 16 \] 3. Substitute this back into the equation: \[ y = -3(x^{2} + 8x + 16) + 8 \] 4. Distribute \(-3\): \[ y = -3x^{2} - 24x - 48 + 8 \] 5. Combine like terms: \[ y = -3x^{2} - 24x - 40 \] Thus, the quadratic function in standard form is: \[ y = -3x^{2} - 24x - 40 \]