determine the quadratic function of the form f(x)=a(x - h)^2 + k whose graph is given on the right.\nf(x)=□
determine the quadratic function of the form f(x)=a(x - h)^2 + k whose graph is given on the right.\nf(x)=□
Answer
Explanation:
Step1: Identify vertex
The vertex - form of a quadratic function is (f(x)=a(x - h)^{2}+k), where ((h,k)) is the vertex of the parabola. From the graph, the vertex ((h,k)=(2,1)), so (h = 2) and (k = 1). Then the function becomes (f(x)=a(x - 2)^{2}+1).
Step2: Find the value of (a)
The parabola passes through the point ((1,0)). Substitute (x = 1) and (y=f(x)=0) into (f(x)=a(x - 2)^{2}+1). We get (0=a(1 - 2)^{2}+1). Simplify the equation: (0=a(-1)^{2}+1), which is (0=a + 1). Solving for (a), we subtract 1 from both sides to get (a=-1).
Answer:
(f(x)=(x - 2)^{2}+1)