Let f(x) = x^2 - 1. A vertical translation of 3 and a horizontal translation of -2 is applied. Write the new function g(x) in the form g(x) = ax^2 + bx + c
Let f(x) = x2- 1To apply a vertical translation, simply add the value to the overall equation. In this case it is positive and thus moves the graph up 3 units:f(x) = x2- 1 + 3 = x2+ 2To apply a horizontal translation, recall the form g(x) = (x-a)2+b; a denotes the horizontal translation, and in this case:g(x) = (x+2)2+ 2 [this translates the graph 2 units to the left]Finally, convert to the form ax2+ bx + c. This can be done by expanding the equation above:g(x) = (x+2)2+ 2= (x+2)(x+2) + 2= x2+ 4x + 4 + 2= x2+ 4x + 6 [ANSWER]
