8. \( \quad 4(x-6)^{2} \)

Did you know this expression represents a quadratic function? Quadratics are like the roller coasters of algebra—full of twists and turns! The vertex form of a quadratic is useful for graphing; here, you can easily find the vertex at \( (6, 0) \) by setting \( (x-6)^2 = 0 \). Isn't it exciting how it opens up different ways to understand the shape of the graph? To further engage with this expression, consider how it can be expanded and transformed! Expanding \( 4(x-6)^{2} \) gives you \( 4(x^{2} - 12x + 36) \) which simplifies to \( 4x^{2} - 48x + 144 \). This form is handy for identifying the coefficients that determine the parabola's width and direction, revealing even more about its behavior on the coordinate plane!