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`.