Question

The parabola \[y=x^2\] is reflected across the \[x\]-axis and then scaled vertically by a factor of \[5\]. what is the equation of the new parabola?

Answer 1

The equation of the new parabola, after reflecting across the x-axis and scaling vertically by a factor of 5, is y = -5x^2.

Step-by-step explanation:

The given parabola is y = x^2. When this parabola is reflected across the x-axis, the sign of the y-coordinate for each point on the parabola is changed, resulting in the equation y = -x^2. This new parabola is then scaled vertically by a factor of 5, which multiplies the y-coordinate of each point by 5. The equation for the transformed parabola now becomes y = -5x^2.