W. Write \( 2 x^{2}+12 x-3 \) in the form \( a(x+b)^{2}+c \), where \( \mathrm{a}, \mathrm{b} \) and c are constal

To rewrite the quadratic expression \( 2x^{2}+12x-3 \) in the form \( a(x+b)^{2}+c \), we first need to factor out \( a \) from the \( x^2 \) and \( x \) terms. Here, \( a = 2 \): \[ 2(x^{2} + 6x) - 3 \] Next, we need to complete the square inside the parentheses. We take the coefficient of \( x \), which is \( 6 \), halve it to get \( 3 \), and square it to obtain \( 9 \): \[ 2(x^{2} + 6x + 9 - 9) - 3 \] This simplifies to: \[ 2((x + 3)^{2} - 9) - 3 \] Distributing the \( 2 \) gives us: \[ 2(x + 3)^{2} - 18 - 3 \] Finally, we combine the constants: \[ 2(x + 3)^{2} - 21 \] Thus, the expression \( 2x^{2}+12x-3 \) in the form \( a(x+b)^{2}+c \) is: \[ 2(x + 3)^{2} - 21 \] Here, \( a = 2 \), \( b = 3 \), and \( c = -21 \).