6.3 Given another function \( \mathrm{E}: y=x^{2} \) and \( \mathrm{F}: y=-2 x^{2} \), deseribe the transformation that moves E to F .

To transform the function \( \mathrm{E}: y = x^{2} \) into the function \( \mathrm{F}: y = -2x^{2} \), we first reflect the graph of \( \mathrm{E} \) across the x-axis. This reflection changes all y-values from positive to negative, resulting in \( y = -x^{2} \). Next, we vertically stretch this reflected graph by a factor of 2, which gives us \( y = -2x^{2} \). The final result captures a downward-opening parabola that is twice as steep compared to the original. This transformation illustrates the power of function manipulation, especially in algebra and precalculus! Understanding these transformations can greatly enhance your graphing skills and provide insights into how different parameters affect the shape and position of graphs. So next time you're sketching a parabola, remember how reflections and stretches can change its look!