Question

Convert each equation to Vertex Formula and Graph each equation showing its vertex.

x2 − 5x + 6=0

Answer 1

vertex form -> y = a(x-h)^2 + k , (h,k) is the vertex point
the standard form -> x^2 + bx +c = 0
x2 − 5x + 6=0
(x-3)(x-2) = 0
the graph intersect x-axis at x=3 and x=2
the value of h = 3+2/2 = 5/2
therefore k = (5/2)^2 -5(5/2) + 6 = 25/4 - 25/2 + 6 = -1/4

so now that we know the value of h and k
y = a(x - 5/2)^2 - 1/4
to find the value of a, just plug the value of point that's passed by the graph. i'll plug x=1, from the standard form, i'll get y=1-5+6 = 2
then i plug that point (1,2)
2=a(1-5/2)^2 - 1/4
2=a(-3/2)^2 -1/4
2=a(9/4)-1/4
a(9/4) = 9/4 -> a=1
finally we have the complete vertex form
y=1(x-5/2)^2 - 1/4 -> y=(x - 5/2)^2 - 1/4

Answer 2

the graph will be looked like this