Question

After transforming f(x) = 2x² +4x + 3 into vertex form, the vertex is easily identifiable. Which ordered pair is the vertex?
(-1, 1)
(0, 3)
(1, 1)
(-3, 0)

Answer 1

The vertex is $(-1,1)$

Explanation:

The equation is $f(x)=2x^{2} +4x+3$

To find the vertex, we need the equation in the form of $f(x)=a (x-h)^{2}+k$

Dividing each term by 2 in the equation $f(x)=2x^{2} +4x+3$

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

Now, completing the square by adding and subtracting 1, we get,

$f(x)=2(x^{2} +2x+1-1+\frac{3}{2} )$

The first three terms can be written as $(x+1)^{2}$,

$f(x)=2[(x+1)^{2}+\frac{1}{2} ]$

Multiplying 2 into the bracket, we get,

$f(x)=2(x+1)^{2} +1$

This equation is of the form $f(x)=a (x-h)^{2}+k$

Now, we shall find the vertex $(h,k)$

Thus, $h=-1$ and $k=1$

Thus, the vertex is $(-1,1)$