Question

Given y=(2x+3)2, choose the standard form of the given quadratic equation

Answer 1

$y=(2x+3)^2 = 4x^2 +12x +9$

Taking 4 out from first two terms, we will get

$y=4(x^2+3x)+9$

Now we divide the coefficient of x by 2 and add and subtract the square of the result, we will get

$y=4(x^2+3x+\frac{9}{4}-\frac{9}{4})+9$

Distributing 4

$y=4(x+\frac{3}{2})^2+9-9$

Cancelling 9

$y=4(x+\frac{3}{2})^2$

And that's the required standard form.