Calculate the vertex of the graph of f(x)=x^2-5x+6. Determine the quadrant where the vertex is .

Expert Answers
hala718 eNotes educator| Certified Educator

f(x) = x^2 - 5x + 6

==> a= 1    b = -5    c= 6

The coordinates of the vertex is:

x = -b/a = 5/1 = 5

y= -(b^2 - 4ac)/4a = - (25 - 4*1*6) / 4 = -1/4

Then the coordinates of the vertix is:

 V = (5, -1/4)

x >0    and y < 0,   then the point V is in the 4th quadrant.

giorgiana1976 | Student

To calculate the vertex of the quadratic, we'll apply the formula:

V (-b/2a ; -delta/4a)

The quadratic function is:

f(x) = ax^2 + bx + c

We'll identify the coordinates a,b,c, of the expression of the function:

a =1 , b = -5, c = 6

Now, we'll calculate the coordinate xV:

xV = 5/1

xV = 5

yV = -delta/4a

yV = (4ac-b^2)/4a

yV = (24-25)/4

yV = -1/4

To determine the quadrant, we'll have to verify where the value of the coordinate x of a point is positive and where the value of the coordinate y is negative.

Since the positive values for x coordinate and negative values for y coordinate are found in the fourth quadrant, we'll conclude that: The coordinates of the vertex of the parable are V(5, -1/4), so, according to the rule, they are located in the fourth quadrant, where xV>0 and yV<0.

neela | Student

f(x) = x^2-5x+6. Or

y = x^2-5x+6. To calculate the vertex of the graph and determine the quadrant of the vertex.

Solution:

 y = x^2-5x+6.

Rewrite this as:

y = x^2-5x+(5/2)^2 -(5/2)^2+6

y = (x-5/2)^2  + (24-25)/4

y = (x-5/2)^2 - 1/4

y+1/4 = (x-5/2)^2.........(1)

So this a parabola like the standard parabola X^2 = 4aY with vertex (X, Y) = (0 , 0 ).

So by comparision eq (1) is a parabola with vertax (x , y)= (5/2 , -1/4), which is in the 4th quadrant.

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