Find the Vertex f(x)=x^2-2x-3

Problem

ƒ(x)=x2−2*x−3

Solution

1. Identify the coefficients of the quadratic function in the standard form ƒ(x)=a*x2+b*x+c

a=1

b=−2

c=−3

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

x=−(−2)/(2*(1))

x=1

3. Substitute the x-coordinate back into the original function to find the y-coordinate.

ƒ(1)=(1)2−2*(1)−3

ƒ(1)=1−2−3

ƒ(1)=−4

4. State the vertex as the ordered pair (x,y)

(1,−4)

Final Answer

Vertex=(1,−4)

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