Answer:
g(x) = h(x - 7) + 5
Step-by-step explanation:
Vertex of a parabola
The turning point (stationary point) of the curve.
- the minimum point of a parabola that opens upwards
- the maximum point of a parabola that opens downwards
To find the series of translations that transform the graph of y = h(x) onto y = g(x), compare the vertices of both graphs.
Vertex of h(x) = (-2, -7)
Vertex of g(x) = (5, -2)
Therefore, y = h(x) has been translated 7 units to the right and 5 units up.
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Therefore:
- h(x) translated 7 units right = h(x - 7)
- h(x - 7) translated 5 units up = h(x - 7) + 5
Therefore, the formula for g(x) in terms of h(x) is:
g(x) = h(x - 7) + 5
Learn more about transformations here:
https://brainly.com/question/27845947
