Answer:
The quadratic equation is: [tex]y=x^2-36[/tex]
Step-by-step explanation:
If the roots of the quadratic equation are "-6" and "6", then it must have the following factors: [tex](x+6)\,\, and \,\,(x-6)[/tex]
Therefore, we can write the equation in factor form as:
[tex]y=a\,(x+6)\,(x-6)[/tex]
where a is a real number constant factor. Now, this equation in standard form will look like:
[tex]y=a\,(x^2+6x-6x-6^2)=a\,(x^2-36)=ax^2-36\,a[/tex]
Therefore, using the information about the leading coefficient being "1" (one), we derive that the constant factor [tex]a[/tex] must be "1". The final expression for the quadratic becomes:
[tex]y=x^2-36[/tex]
