Algebra 2 2-1 Savvas

Question

Write the equation g(x) in vertex form of a quadratic function for the transformations given the function f(x)=x^2. Let g(x) be the function whose graph is a reflection in the​ x-axis and translated 3 units right of the graph of f(x).

Answer 1

Hi Lopez,

Background: Vertex form of f(x) = x² is f(x) = (x - h)² + k where (h, k) is the vertex. Reflecting in the x axis means changing f(x) to -f(x)

So applying the the translation first (3 to the right) we get a vertex of (3, 0). So, g(x) = (x - 3)² + 0

Next, we want the opposite of f(x), so the function we are looking for is g(x) = -(x - 3)² + 0

Of course, adding zero doesn't change anything so we can leave it as g(x) = -(x - 3)²

Playing around with quadratic functions using Desmos Graphing Calculator can teach you a lot about these transformations.