Find the Vertex f(x)=2x^2+4x-6

Problem

ƒ(x)=2*x2+4*x−6

Solution

1. Identify the coefficients of the quadratic function in the form ƒ(x)=a*x2+b*x+c where a=2 b=4 and c=−6

2. Calculate the xcoordinate of the vertex using the formula x=(−b)/(2*a)

x=(−4)/(2*(2))

3. Simplify the expression to find the value of x

x=−1

4. Substitute x=−1 back into the original function to find the ycoordinate of the vertex.

ƒ*(−1)=2*(−1)2+4*(−1)−6

5. Evaluate the function to find the value of y

ƒ*(−1)=2−4−6

ƒ*(−1)=−8

Final Answer

Vertex=(−1,−8)

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