Question

The parabola y = x² is reflected across the x-axis and then scaled vertically by a factor of 5. What is the equation of the new parabola?

a) y = -5x²

b) y = 5x²

c) y = -25x²

d) y = 25x²

Answer 1

The new parabola given by reflecting y = x² across the x-axis and then scaling vertically by a factor of 5 is y = -5x².

Step-by-step explanation:

The original parabola is given by the equation y = x². When the parabola is reflected across the x-axis, the sign of the y values is reversed, resulting in the equation y = -x². Following this, the parabola is scaled vertically by a factor of 5. This means that the y-values are multiplied by 5, changing the equation to y = 5(-x²) which simplifies to y = -5x². Therefore, the correct equation for the new parabola after the reflection and scaling is y = -5x².