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Sonbull [250]
3 years ago
11

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

Mathematics
1 answer:
jolli1 [7]3 years ago
7 0

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)

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