write an equation for the function whose graph is shown to the right. the graph shows a transformation of a…
write an equation for the function whose graph is shown to the right. the graph shows a transformation of a common function. an equation for the function of the given graph is (type an equation using x and y as the variables. use integers or decimals for any numbers in the equation.)
Answer
Explanation:
Step1: Identify the common - function
The graph appears to be a transformation of the parabola (y = x^{2}).
Step2: Determine the vertex
From the viewing - window ([- 10,10,1]) by ([-1,7,1]), assume the vertex of the parabola is ((h,k)). If the vertex is at ((2, - 1)) (by observing the position of the lowest point of the parabola). The general form of a parabola in vertex form is (y=a(x - h)^{2}+k).
Step3: Find the value of (a)
Let's assume another point on the parabola, say ((3,0)) (by estimating from the graph). Substitute (x = 3), (y = 0), (h = 2), and (k=-1) into (y=a(x - h)^{2}+k). We get (0=a(3 - 2)^{2}-1), which simplifies to (0=a - 1), so (a = 1).
Answer:
(y=(x - 2)^{2}-1)