150k views
5 votes
Write the quadratic equation whose roots are -6 and 6, and whose leading coefficient is 1 .

User PeterBelm
by
8.3k points

1 Answer

6 votes

Answer:

The quadratic equation is:
y=x^2-36

Explanation:

If the roots of the quadratic equation are "-6" and "6", then it must have the following factors:
(x+6)\,\, and \,\,(x-6)

Therefore, we can write the equation in factor form as:


y=a\,(x+6)\,(x-6)

where a is a real number constant factor. Now, this equation in standard form will look like:


y=a\,(x^2+6x-6x-6^2)=a\,(x^2-36)=ax^2-36\,a

Therefore, using the information about the leading coefficient being "1" (one), we derive that the constant factor
a must be "1". The final expression for the quadratic becomes:


y=x^2-36

User Bishnu Rawal
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories