Find the x and y Intercepts y=x^4-25

Problem

y=x4−25

Solution

1. Find the y-intercept by setting x=0 in the equation.

y=0−25

y=−25

2. Find the x-intercepts by setting y=0 and solving for x

0=x4−25

3. Isolate the variable by adding 25 to both sides of the equation.

x4=25

4. Take the fourth root of both sides, remembering to include both the positive and negative roots.

x=±√(4,25)

5. Simplify the radical by rewriting 25 as 5 and reducing the index.

x=±√(4,5)

x=±√(,5)

Final Answer

x-intercepts: *(±√(,5),0), y-intercept: *(0,−25)

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