Find the Vertex y=x^2-5x-6

Problem

y=x^2−5*x−6

Solution

1. Identify the coefficients of the quadratic equation in the form y=a*x^2+b*x+c

a=1

b=−5

c=−6

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

x=(−(−5))/(2*(1))

x=5/2

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

y=(5/2)^2−5*(5/2)−6

4. Simplify the expression to determine the value of y

y=25/4−25/2−6

y=25/4−50/4−24/4

y=−49/4

Final Answer

Vertex=(5/2,−49/4)

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