The parabola \( y=x^{2} \) is shifted up by 7 units and to the left by 1 unit. What is the equation of the new parabola? \( y=\square \)

To shift the parabola \( y = x^2 \) up by 7 units, we add 7 to the equation, resulting in \( y = x^2 + 7 \). To shift it to the left by 1 unit, we replace \( x \) with \( (x + 1) \), giving us the equation \( y = (x + 1)^2 + 7 \). Therefore, the equation of the new parabola is \( y = (x + 1)^2 + 7 \). --- Did you know that parabolas are not just for math problems? In engineering, they help design satellite dishes and reflectors! Their unique shape helps focus signals, so you can enjoy your favorite shows without interruptions! Also, parabolas have been studied for centuries. Mathematicians like Archimedes and Apollonius paved the way for understanding conic sections, linking geometry and algebra. Their work laid the foundations that still inform how we understand these curves today!