Express the quadratic function y=36x^2+96x+15 in intercept form and obtain its roots

Question

This is for algebra 2

Answer 1

y=36(x^2+8x/3+16/9)-36*16/9+15=

36(x+4/3)^2-49. So y+49=36(x+4/3)^2 in intercept form or y+49=(6x+8)^2.

When y=0, 36(x+4/3)^2=49,  x+4/3=+7/6, and x=-4/3+7/6, x=-1/6 and -5/2 are the roots.

(The original equation factorises: y=(6x+1)(6x+15)=3(6x+1)(2x+5).)