The turning point of the function represented by f(x) = x^2 -6x+7 has coordinates (3,-2). Find the coordinates of the turning point of the function defined by g(x)= f(x)+2. explain how you arrived at your answer
f(x) vs f(x) + 2
everything has just moved up vertically by 2 units
so (3,-2) ---> (3,0)
To find the coordinates of the turning point of the function g(x) = f(x) + 2, we need to consider that adding a constant term like 2 simply shifts the graph of the function vertically, without affecting the shape of the graph.
The turning point of a quadratic function is the vertex of its graph. In general, for the quadratic function f(x) = ax^2 + bx + c, the x-coordinate of the turning point can be found using the formula x = -b / (2a).
In this case, the function f(x) = x^2 - 6x + 7 has a turning point with x-coordinate x = -(-6) / (2*1) = 6 / 2 = 3. Therefore, we have already been given that the x-coordinate of the turning point is 3.
Since adding a constant term does not affect the x-coordinate of the turning point, the x-coordinate of the turning point of g(x) = f(x) + 2 will also be 3.
For the y-coordinate, we can substitute the x-coordinate (3) into the original function f(x) to find the corresponding y-coordinate. Therefore, we evaluate f(3) = (3)^2 - 6(3) + 7 = 9 - 18 + 7 = -2.
Now, we can add 2 to the y-coordinate obtained from f(3), as g(x) = f(x) + 2. Thus, the y-coordinate of the turning point of g(x) will be -2 + 2 = 0.
Therefore, the coordinates of the turning point of the function g(x) = f(x) + 2 are (3,0).