Question

What were the transformations from f(x) = x^2 to f(x) = -7(x - 9)^2 + 3?

a) Shifted left 9 units, shifted up 3 units, reflected over the x-axis, vertically stretched by a factor of 7
b) Shifted right 9 units, shifted up 3 units, vertically compressed by a factor of 7
c) Shifted right 9 units, shifted up 3 units, reflected over the y-axis, vertically compressed by a factor of 7
d) Shifted right 9 units, shifted up 3 units, reflected over the x-axis, and vertically stretched by a factor of 7

Answer 1

The correct transformations from f(x) = x^2 to f(x) = -7(x - 9)^2 + 3 are shifted right 9 units, shifted up 3 units, reflected over the x-axis, and vertically stretched by a factor of 7.

Step-by-step explanation:

The question is about identifying the transformations applied to the function f(x) = x^2 to get the function f(x) = -7(x - 9)^2 + 3. The correct transformations are:

• Shifted right 9 units (since the function is f(x - 9), which means the graph moves 9 units to the right).
• Shifted up 3 units (because of the +3 at the end of the function, which moves the graph up by 3 units).
• Reflected over the x-axis (the negative sign in front of 7 indicates reflection across the x-axis).
• Vertically stretched by a factor of 7 (the leading coefficient of 7 increases the steepness of the graph by a factor of 7).

Therefore, the correct answer is (d): Shifted right 9 units, shifted up 3 units, reflected over the x-axis, and vertically stretched by a factor of 7.