SOLUTION: rewrite function f(x)=-1/3x2-2x-9 in the form f(x)=a(x-h)2+k give x and y intercepts give domain and range

Question 694630: rewrite function f(x)=-1/3x2-2x-9 in the form f(x)=a(x-h)2+k
give x and y intercepts
give domain and range
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
in the form

Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

Start with the given equation

......set
...use quadratic formula to solve for

....so, we have two complex solutions, it means there is no real solutions and there is no

and ......set

....... is at (,)

see it on a graph:

domain:

range:

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
rewrite function
f(x)=-1/3x2-2x-9 in the form f(x)=a(x-h)2+k
y = (-1/3)(x^2 - [(-2)/(-1/3)]x + ?) - 9 -(-1/3)(?)
-----
Complete the square:
y = (-1/3)(x^2 +(6)x + 9) - 9 -(-1/3)9
------
Factor:
y = (-1/3)(x+3))^2 - 9 + 3
----
y = (-1/3)(x+3))^2 - 6
------------
give x and y intercepts
x-intercept:: ?
Let y = 0 ; Use the Quadratic Formula to solve for "x".
-----
y-intercept:: ?
Let x = 0, then y = -9
-----
Domain: All Real Numbers
---
Range = ?
Vertex is at ((-3),-6)
Range is All Real Numbers <= -6
=====================================
Cheers,
Stan H.
====================

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