Graph f(x)=(x-1)^2-4

Problem

ƒ(x)=(x−1)2−4

Solution

1. Identify the function type and its parent form. The function ƒ(x)=(x−1)2−4 is a quadratic function in vertex form, ƒ(x)=a*(x−h)2+k

2. Determine the vertex (h,k) from the equation. By comparing ƒ(x)=(x−1)2−4 to the vertex form, the vertex is (1,−4)

3. Find the y-intercept by evaluating the function at x=0

ƒ(0)=(0−1)2−4

ƒ(0)=1−4=−3

The y-intercept is (0,−3)

4. Find the x-intercepts by setting ƒ(x)=0 and solving for x

(x−1)2−4=0

(x−1)2=4

x−1=±2

x=3,x=−1

The x-intercepts are (3,0) and (−1,0)

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

x=1

6. Plot the points and draw a smooth parabola opening upwards since the leading coefficient a=1 is positive.

Final Answer

ƒ(x)=(x−1)2−4

Want more problems? Check here!