Expert: Paul Klarreich - 10/8/2007

Question
how do I solve for "k" in the formula
f(x)=-3x^2+4x+5 when trying to find the vertex

Answer
Questioner:   Bobby
Category:  Advanced Math
Private:  No
 
Subject:  vertex
Question:  how do I solve for "k" in the formula
f(x)=-3x^2+4x+5 when trying to find the vertex
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Hi, Bobby,

If you want to solve for 'k', you must have one somewhere in your equation.  You don't.

Since you did say you are finding the vertex, I'll assume that:

1. You want the coordinates, x and y, of the vertex, and

2. You are calling the vertex  (h,k), so k is the y-coordinate.  

I think that once you realize  k is the y-coordinate, the rest will be easy.

Start by using the formula:

h = -b/2a

[proof on request]

In this case,  a = -3,  b = 4.

h = -(4)/2(-3) = -4/-6 =  +2/3.

Now substitute that, since  h is the x-coordinate of the vertex, and we ALWAYS get the y-coordinate by substitution.

y = k = - 3(2/3)^2 + 4(2/3) + 5

k = - 3(4/9) + 8/3 + 5

k = - 4/3 + 8/3 + 5

k = 4/3 + 5

k = 4/3 + 15/3 = 19/3