Question

Write 4x2 + 16x - 9 in vertex form.

Answer 1

We know that the vertex form of any quadratic function is the form:

$f (x) = a(x - h)^2 + k$

The given quadratic function is $f(x) = 4x^2 + 16x - 9$

To convert it into the vertex form we will have to complete the square of the quadratic expression given here which may be done as shown below:

$f(x) = 4x^2 + 16x - 9 =4(x^2+4x)-9$

Thus, $f(x)=4(x^2+4x+\mathbf{4})-\boldsymbol{\mathbf{16}}-9$ (This is because adding a 4 inside the parentheses to complete the square is equivalent to adding 16 to the whole expression and thus we need to subtract 16 from the overall expression.)

$\therefore f(x)=4(x+2)^2-25$

The above is the vertex form of the original given function, $f(x) = 4x^2 + 16x - 9$.