Question 4 Simplify the following quadratic equations and rewrite them in standard form. After rewritten, identif) \( a, b \), and \( c \) terms. \( g(x)=3 x^{2}-2(x-1) \) Standard Form: \( a=\square, b=\square \) Question Help: \( D \) Post to forum Submit Question

To simplify \( g(x) = 3x^2 - 2(x-1) \), first distribute the \(-2\): \[ g(x) = 3x^2 - 2x + 2 \] Now, write it in standard form, which is \( ax^2 + bx + c \). So, \( g(x) = 3x^2 - 2x + 2 \). Thus, \( a=3, b=-2, c=2 \). Quadratics like this describe parabolas, and they can model a variety of real-world scenarios like projectile motion! Whenever something is launched into the air, equations like this help predict the height at any given time, showing their usefulness in physics and engineering. When working on simplifying quadratics, watch out for common pitfalls like forgetting to distribute the minus sign correctly or combining like terms inaccurately. A simple way to avoid errors is to write each step clearly and check your calculations twice. Happy simplifying!