Determine whether the equation defines \( y \) as a function of \( x \). Doe \( 2 x^{2}+8 x-8 \) Des equation define \( y \) as a function of \( x \) ? Yes

To determine if the equation \( 2x^2 + 8x - 8 = y \) defines \( y \) as a function of \( x \), we need to check if for each \( x \) value, there is only one corresponding \( y \) value. Since this is a quadratic equation, it can be rewritten in the standard form. Quadratic equations typically have a parabolic shape, which means that for certain \( x \) values, there may be two different \( y \) values. Therefore, this equation does not define \( y \) as a function of \( x \). Although the previous deduction was incorrect in concluding that it defines \( y \) as a function, many quadratic functions can yield specific values if we restrict the domain. For instance, if we only consider the vertex or a specific interval on the \( x \)-axis, then we can treat it as a function over that limited range. Always keeping an eye on the domain can make a difference!