Question

Write the quadratic equation whose roots are -6 and 6, and whose leading coefficient is 1 .

Answer 1

Answer:

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

Step-by-step 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:

$y=x^2-36$