justine graphs the function $f(x)=(x - 7)^2-1$. on the same grid, she graphs the function $g(x)=(x +…

justine graphs the function $f(x)=(x - 7)^2-1$. on the same grid, she graphs the function $g(x)=(x + 6)^2-3$. which transformation will map $f(x)$ on to $g(x)$?\nleft 13 units, down 2 units\nright 13 units, down 2 units\nleft 13 units, up 2 units\nright 13 units, up 2 units

justine graphs the function $f(x)=(x - 7)^2-1$. on the same grid, she graphs the function $g(x)=(x + 6)^2-3$. which transformation will map $f(x)$ on to $g(x)$?\nleft 13 units, down 2 units\nright 13 units, down 2 units\nleft 13 units, up 2 units\nright 13 units, up 2 units

Answer

Explanation:

Step1: Analyze x - coordinate transformation

For a quadratic function in vertex - form (y=(x - h)^2 + k), the vertex of (f(x)=(x - 7)^2-1) is ((7,-1)) and the vertex of (g(x)=(x + 6)^2-3) is ((-6,-3)). To find the horizontal shift, we calculate the difference in the x - coordinates of the vertices: (-6-7=-13). A negative difference means a shift to the left by 13 units.

Step2: Analyze y - coordinate transformation

To find the vertical shift, we calculate the difference in the y - coordinates of the vertices: (-3-(-1)=-3 + 1=-2). A negative difference means a shift down by 2 units.

Answer:

left 13 units, down 2 units