Question

Which phrase best describes the translation from the graph y = (x â€"" 5)2 7 to the graph of y = (x 1)2 â€"" 2?.

Answer 1

The vertex of the parabola will move from (5, 7) to (-1, -2).

Given to us,

Equation 1, h(x) = (x-5)²+7,

Equation 2, g(x) = (x+1)²-2,

graph of parabola

For both the given equations, we will get a graph of parabola(as in the image below),

h(x) = (x-5)²+7, represented in red;

g(x) = (x+1)²-2, represented in blue;

Coordinates

Also, we know for a parabola, the coordinates of the vertex of a parabola are given by, f(x) = (x - h)² + k, where (h, k) are coordinates of a vertex of a parabola.

Using the same,

h(x) = (x-5)²+7, coordinates of a vertex of this parabola are (5, 7);

g(x) = (x+1)²-2, coordinates of a vertex of this parabola are (-1, -2);

Therefore, the vertex of the parabola will move from (5, 7) to (-1, -2).

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