Answer:
y = -5x²
Step-by-step explanation:
You want the equation of the parabola y = x² after reflection over the x-axis and vertical scaling by a factor of 5.
A function f(x) that is vertically scaled by a factor of k will be k·f(x). When a vertical reflection is also involved, the sign of k will be negative.
Your reflected, scaled function will have k = -5:
y = -5x²
The original parabola y = x², when reflected across the x-axis and scaled vertically by 5, results in the new equation y = -5x².
The original parabola is given by the equation y = x². When this parabola is reflected across the x-axis, the y-values change sign, hence the new equation will be y = -x².
Further, when this reflected parabola is scaled vertically by a factor of 5, each y-value is multiplied by 5. Therefore, the equation of the new parabola after scaling becomes y = -5x².
Reflection across the x-axis inverts the sign of the y-coordinates of the parabola. So, the parabola which opens upwards (y = x²) will now open downwards (y = -x²). The vertical scaling by a factor of 5 amplifies the stretch of the parabola, making it 'wider' by multiplying the y-values by 5.
