Help me find the vertex of the parabola please.?

Question

g(x) = x2 - 9x + 2

Answer 1

Without calculus:

The vertex falls between the roots.

x1 = 8.772

x2 = 0.228

(I just plugged that into a quadratic solver)

Find the x value that is halfway between (x1 + x2)/2

= 4.5

so the vertex is at (4.5, y)  

Solve for y by plugging it back into the original equation

(4.5)^2 - 9(4.5) + 2 = -18.25]

so the vertex is at ( 4.5, -18.25)

Using calculus:

d/dx g(x) = 2x - 9.

2x-9 = 0, x = 4.5.

And proceed as above to find the y-coordinate

(Properly I should take the second derivative and check to make sure it's not an inflection point, but It's a parabola, so why bother)

Answer 2

Nice g-string.

Answer 3

the x coordinate of a parabola's vertex is -b/2a.

so a =1, b=-9 and c=2

-b/2a = -(-9)/2(1) = 9/2

plug that in for x in the equation:

g(9/2) = (9/2)² - 9(9/2) +2

g(9/2) = (81/4) - (81/2) +2

g(9/2) = (81/4) - (162/4) + (8/4)

g(9/2) = -73/4 = -18.25

vertex = (9/2 , -73/4) or (4.5, -18.25)

Answer 4

parabola... y = ax^2 + bx + c

The vertex x-value is x = -b/(2a) = -(-9)/(2*1) = 9/2

y = (9/2)^2 - 9(9/2) + 2 = -73/4

The vertex point is (9/2, -73/4)

Take care,

David