Question

Write the function that is reflected over the x axis, vertical stretch by a factor of 2, has a horizontal shift 3 units to the left, and a vertical shift 7 units down in vertex form f(x)=a(x−h)2+k .

Answer 1

The function that satisfies the given conditions is f(x) = 2(x+3)^2 - 7.

Step-by-step explanation:

In this function, the reflection over the x-axis is achieved by the negative sign in front of the entire function. The vertical stretch by a factor of 2 is represented by the coefficient 2 in front of the squared term. The horizontal shift 3 units to the left is achieved by the horizontal shift of the vertex, which is represented by the value -3 inside the parentheses. Finally, the vertical shift 7 units down is represented by the constant term -7 at the end of the function.