Find the Roots (Zeros) y=1/4x^2-2x-12

Problem

y=1/4*x2−2*x−12

Solution

1. Set the equation to zero to find the roots of the function.

0=1/4*x2−2*x−12

2. Multiply the entire equation by 4 to eliminate the fraction and simplify the quadratic.

0=x2−8*x−48

3. Identify two numbers that multiply to −48 and add to −8 These numbers are −12 and 4

0=(x−12)*(x+4)

4. Apply the Zero Product Property by setting each factor equal to zero.

x−12=0

x+4=0

5. Solve for x in each linear equation to find the roots.

x=12

x=−4

Final Answer

x=12,−4

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