Question

Write the function in vertex form.
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Answer 1

Answer:

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

Step-by-step explanation:

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