write the equation the graph of y=x^2 is vertically stretched by a factor of 9, and the resulting graph is reflected across the x-axis
wrong again
y = -9x^2
Apologies for the incorrect previous response. You are correct, when the graph of y = x^2 is vertically stretched by a factor of 9 and reflected across the x-axis, the equation becomes:
y = -9x^2
To vertically stretch the graph of y = x^2 by a factor of 9, we replace y with 9y:
9y = (x^2)
To reflect the resulting graph across the x-axis, we need to change the sign of y. Therefore, the equation becomes:
-9y = (x^2)
Simplifying the equation, we can divide both sides by -9:
y = -(1/9)(x^2)
Therefore, the equation of the graph after it is vertically stretched by a factor of 9 and reflected across the x-axis is:
y = -(1/9)(x^2)