Question

Which equation is y= -6x^2 +3x+2 rewritten in vertex form?

y=-6(x-1)^2+8
y=-6(x+1/4)^2+13/8
y=-6(x-1/4)^2+19/8
y=-6(x-1/2)^2+7/2

Answer 1

`\boxed{\,\bold{y=-6\left(x-\frac14\right)^2+\,\frac{19}8}\,}`

Explanation:

`y= -6x^2 +3x+2\\\\y=-6\big(x^2-\frac16\cdot3x-\frac16\cdot2\big)\\\\y=-6\big(x^2-\frac12x-\frac13\big)\\\\ y=-6\big(\underline{x^2-2\cdot x\cdot\frac14+(\frac14)^2}-(\frac14)^2-\frac13\big)\\\\ y=-6\big((x-\frac14)^2-\frac1{16}-\frac13\big)\\\\ y=-6(x-\frac14)^2+\frac38+2\\\\ \underline{y=-6(x-\frac14)^2+\frac{19}8}`