Question

The parent function for a quadratic is represented by f(x) = x2

Jacob states that only a vertical and horizontaltranslation would be represented by
f(x) = (x + 7)2 – 2.Is he correct? Jusitfy

Answer 1

Jacob is partially correct. The equation f(x) = (x + 7)² – 2 represents a vertical translation of 7 units to the left and a horizontal translation of 2 units downward.

Step-by-step explanation:

Jacob is partially correct. The parent function for a quadratic is represented by f(x) = x². The equation f(x) = (x + 7)² – 2 represents a vertical translation of 7 units to the left and a horizontal translation of 2 units downward.

The equation f(x) = x² represents the basic shape and orientation of a quadratic function. When we add or subtract values within the function, we are performing vertical or horizontal translations respectively. In this case, adding 7 within the function shifts the graph 7 units to the left, and subtracting 2 moves the graph 2 units downward.