Question

what is the vertex of the quadratic function f(x) =2x^2 + 4x + 3

Answer 1

Given a quadratic equation ax^2+bx+c, the x-coordinate of the vertex is given as:

$-\frac{b}{2a}$

Since the quadratic equation given is:

$2x^2+4x+3$

It follows that: a=2, b=4 and c=3.

Substitute these values into the formula for the x-coordinate of the vertex:

$\begin{gathered} -\frac{b}{2a} \\ \Rightarrow-\frac{4}{2(2)}=-\frac{4}{4}=-1 \end{gathered}$

Hence, the x-coordinate of the vertex is -1.

To get the y-coordinate of the vertex, substitute the x-coordinate into the equation representing the function:

$\begin{gathered} f(x)=2x^2+4x+3 \\ \text{Substitute x=-1} \\ f(-1)=2(-1)^2+4(-1)+3 \\ \Rightarrow f(-1)=2(1)-4+3=2-4+3=1 \end{gathered}$

Hence, the y-coordinate of the vertex is 1.

It follows that the vertex is (-1,1).

The correct option is B.