<s>[INST] How do I get the equation for this parabola in standard form? How do I get the equation for this parabola in standard form?
$ y = f(x)= 2x^2+3x-2$
 [/INST] If you mean vertex form, you can complete the square.
$$\begin{align}f(x) &= 2x^2 + 3x - 2 \\
                    &= 2\left(x^2+\frac{3}{2}x\right) -2 \\
                    &= 2\left(x^2+\frac{3}{2}x+\frac{9}{16}-\frac{9}{16}\right) -2\\
                    &= 2\left(x^2 +\frac{3}{2}x+\frac{9}{16}\right) -2\left(\frac{9}{16}\right)-2\\
                    &= 2\left(x+\frac{3}{4}\right)^2 - \frac{25}{8}\end{align}$$
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