Graph y=(x-2)^2-1

Problem

y=(x−2)2−1

Solution

1. Identify the form of the equation. This is a quadratic function in vertex form, y=a*(x−h)2+k where (h,k) is the vertex.

2. Determine the vertex. Comparing y=(x−2)2−1 to the vertex form, we find h=2 and k=−1

V=(2,−1)

3. Find the y-intercept by setting x=0

y=(0−2)2−1

y=4−1=3

4. Find the x-intercepts by setting y=0

0=(x−2)2−1

(x−2)2=1

x−2=±1

x=1,x=3

5. Identify the axis of symmetry. The axis of symmetry is the vertical line passing through the vertex.

x=2

6. Plot the points (2,−1) (0,3) (1,0) and (3,0) then draw a smooth parabola opening upward since a=1 is positive.

Final Answer

y=(x−2)2−1

Want more problems? Check here!