Final Vertex Question: f(x) = 3x^2-14x+15?

Question

Find the vertex of the parabola:

Answer will be in (#/#,#/#) form

Answer 1

(7/3, -4/3)

Method: There are several ways to find the x-coordinate of the vertex, but by far the simplest is to realize that it always coincides with the maximum/minimum of the parabola. So we take the derivative of 3x²-14x+15 to get 6x-14, which we set equal to zero and solve to get x=14/6=7/3. Then we just plug that into the original equation to find the value of y.

Answer 2

The zeros are always [-b +/- sqrt( discriminant )]/2*a, so the vertex, where they balance, is at -b/2*a, where b is the co-efficient of x, and a, that of x^2.

This is the value of x. To find the value of y, y=f(x).

Answer 3

f'(x) = 6x - 14
0 = 6x - 14
14 = 6x
7/3 = x

f(x) = 3(7/3)^2 - 14(7/3) + 15
f(x) = 3(49/9) - (98/3) + 15
f(x) = 49/3 - 98/3 + 15
f(x) = 15 - 49/3
f(x) = -4/3

The vertex is (7/3, -4/3) or (2.33, -1.33)

Answer 4

f(x) = 3x^2 - 14x + 15

x = (-b)/(2a)
x = (-(-14))/(2(3))
x = (14/6)
x = (7/3)

f(7/3) = 3(7/3)^2 - 14(7/3) + 15
f(7/3) = 3(49/9) - (98/3) + 15
f(7/3) = (49/3) - (98/3) + 15
f(7/3) = ((49 - 98)/3) + 15
f(7/3) = (-49/3) + 15
f(7/3) = (-49/3) + (45/3)
f(7/3) = (-49 + 45)/3
f(7/3) = (-4/3)

ANS : ((7/3), (-4/3))

Answer 5

vertex is (-b/2a,-D/4a)
= (7/3,-4/3)

Answer 6

f(x)=(3x-5)(x-3)