Questions: Re-write the quadratic function below in Standard Form y=-7(x-1)^2-1

Solution Steps

To convert a quadratic function from vertex form to standard form, we need to expand the squared term and simplify. The vertex form of a quadratic is given by \( y = a(x-h)^2 + k \). To convert it to standard form \( y = ax^2 + bx + c \), we expand the squared term and distribute the coefficient \( a \).

The given quadratic function is in vertex form: \[ y = -7(x-1)^2 - 1 \]

To convert to standard form, we first expand the squared term: \[ (x-1)^2 = x^2 - 2x + 1 \]

Next, distribute the \(-7\) across the expanded terms: \[ -7(x^2 - 2x + 1) = -7x^2 + 14x - 7 \]

Add the constant term \(-1\) to the expression: \[ y = -7x^2 + 14x - 7 - 1 \]

Combine like terms: \[ y = -7x^2 + 14x - 8 \]

Final Answer