Question

What is the equation of the following graph in vertex form? HELP PLS

Answer 1

Answer:

y = (x - 2)^2 + 1

Step-by-step explanation:

The general equation of a parabola in vertex form is y-k = (x-h)^2.  Here, we can see immediately from the graph that the vertex is at (2, 1).  Thus, the equation of this particular parabola takes the form y - 1 = a(x - 2)^2.  We must still determine the value of a.  Note that the graph goes through (0, 5).  Thus, 5 - 1 = a(0 - 2)^2, or

4 = 4a.  Thus, a = 1, and the equation of this parabola is y - 1 = (x - 2)^2, or, after simplification, y = (x - 2)^2 + 1.