## anonymous 5 years ago Find the quadratis equation having the given roots. {-3,-7}

1. anonymous

lol loki, that's a funny face :D

2. anonymous

mr. track, if alpha and beta are the roots of a quadratic equation, then that quadratic may be factored as$(x-\alpha)(x-\beta)$Expanding, you have,$x^2-(\alpha+\beta)x+\alpha \beta$Here, $\alpha = -3$and $\beta=-7$so your equation is$x^2-(-3+-7)x+(-3)(-7)$$=x^2+10x+21$

3. anonymous

That is, since your roots are -3 and -7, when you factor the quadratic that allows for this to be the case, you'd have$(x-(-3)(x-(-7))=(x+3)(x+7)$

4. amistre64

"Find the quadratic equation having the given roots." Wouldnt that be find "a" quadratic equation given those roots? cause we can have the same root, and the same axis of symmetry, but e different vertex along the axis which would constitute a different equation with the same root. right?

5. amistre64

*but have a different vertex...

6. amistre64

the only way I know of to pinpoint a quadratic is with 3 known points.

7. amistre64

if we use k as a constant then: all the parabolas that fit the equation would be: k(x^2 +10x +21) right?

8. anonymous

Yes, that's correct. I read the question as 'a' parabola...was late.