SOLUTION: Complete the square for each equation and determine the vertex and the maximum and minimum value of the function for which the vertex occurs: a) y=6x^2+12x-18 b) y=4x^2-16+10

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Complete the square for each equation and determine the vertex and the maximum and minimum value of the function for which the vertex occurs: a) y=6x^2+12x-18 b) y=4x^2-16+10      Log On


   

Question 1132947: Complete the square for each equation and determine the vertex and the maximum and minimum value of the function for which the vertex occurs:
a) y=6x^2+12x-18
b) y=4x^2-16+10
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a)
y=6x%5E2%2B12x-18+
y=%286x%5E2%2B12x%29-18+
y=6%28x%5E2%2B2x%29-18+
y=6%28x%5E2%2B2x%2Bb%5E2%29-6b%5E2-18+...take half of coefficient of x or b:2%2F2=1
y=6%28x%5E2%2B2x%2B1%5E2%29-6%2A1%5E2-18+
y=6%28x%2B1%29%5E2-6-18+
y=6%28x%2B1%29%5E2-24+=>h=-1 and k=-24
the vertex occurs at (-1,-24)



b)
y=4x%5E2-16%2B10
y=4x%5E2-6
we cannot complete the square for this equation
use zero value for x to find minimum where the vertex occurs
y=4%2A0%5E2-6
y=-6
=>the vertex occurs at (0,-6)