SOLUTION: 2. Given the equation f(x)=-3(x-4)(x+8), determine the following algebraically. please show your work. x-intercepts y-intercept Equation of the axis of symmetry Vertex 3

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 2. Given the equation f(x)=-3(x-4)(x+8), determine the following algebraically. please show your work. x-intercepts y-intercept Equation of the axis of symmetry Vertex 3      Log On


   

Question 1198644: 2. Given the equation f(x)=-3(x-4)(x+8), determine the following algebraically. please show your work.
x-intercepts
y-intercept
Equation of the axis of symmetry
Vertex
3.Convert the following from standard form to vertex form by completing the square.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Given the equation +f%28x%29=-3%28x-4%29%28x%2B8%29, determine the following algebraically. please show your work.

+x-intercepts- set +f%28x%29=0
+-3%28x-4%29%28x%2B8%29=0
+x=4
+x=-8
+x-intercepts: (+4,+0), (+-8,+0)

+y-intercept:- set +x=0
+f%280%29=-3%280-4%29%280%2B8%29=96

Equation of the axis of symmetry
The axis of symmetry equation of a parabola whose vertex is (+h,++k) and opens up/down is +x+=+h.
so, first convert to vertex form (3.)
+x+=-2
Vertex:(+h, +k) =(+-2,++108)
3.Convert the following from standard form to vertex form by completing the square.
+f%28x%29=-3%28x-4%29%28x%2B8%29
+f%28x%29=-3+x%5E2+-+12x+%2B+96
+f%28x%29=-3+%28x%5E2+%2B+4x+%29%2B+96
+f%28x%29=-3+%28x%5E2+%2B+4x+%2B2%5E2%29-%28-3%29%2A2%5E2%2B+96
+f%28x%29=-3+%28x+%2B2%29%5E2%29%2B12%2B+96
+f%28x%29=-3+%28x+%2B2%29%5E2%29%2B108
so +h=-2, +k=108