Answer:
[tex]y=2x^2-4x-16[/tex]
Step-by-step explanation:
Factored form of a quadratic equation:
[tex]y=a(x-r_1)(x-r_2)[/tex]
where:
- a is the leading coefficient
- [tex]r_1[/tex] and [tex]r_2[/tex] are the roots
Given:
- [tex]a = 2[/tex]
- [tex]r_1=4[/tex]
- [tex]r_2=-2[/tex]
Substitute the given values into the formula and expand:
[tex]\implies y=2(x-4)(x-(-2))[/tex]
[tex]\implies y=2(x-4)(x+2)[/tex]
[tex]\implies y=2(x^2+2x-4x-8)[/tex]
[tex]\implies y=2x^2-4x-16[/tex]
