Question

Write the function in vertex form.
​

Answer 1

`\boxed{\bold{y=\frac94\left(x+\frac23\right)^\big{\bold2}-\,2}}`

Explanation:

`y=\frac94x^2+3x-1\\\\y=\frac94(x^2+\frac49\cdot3x-\frac49)\\\\y=\frac94\big(\underline{x^2+2\cdot x\cdot\frac23+(\frac23)^2}-(\frac23)^2-\frac49\big)\\\\y=\frac94\big((x+\frac23)^2-\frac49-\frac49\big)\\\\y=\frac94(x+\frac23)^2-1-1\\\\\underline{y=\frac94(x+\frac23)^2-2}`