Question

which best describes the transformation that occurs from the graph of ( f(x) = x^2 ) to ( g(x) = (x + 3)^2 + 4 )?

• left 3, up 4
• right 3, down 4
• left 3, down 4
• right 3, up 4

Explanation:

For a quadratic function in vertex form \(g(x) = (x - h)^2 + k\) compared to the parent function \(f(x) = x^2\):

• \(h\) shifts the graph horizontally: if \(h < 0\) (written as \(x + |h|\)), it shifts left \(|h|\) units. Here, \(h = -3\), so shift left 3 units.
• \(k\) shifts the graph vertically: if \(k > 0\), it shifts up \(k\) units. Here, \(k = 4\), so shift up 4 units.

Answer:

left 3, up 4