SOLUTION: Find the vertex and intercepts for each parabola, and sketch its graph. y= -x^2 -3x - 2

Algebra ->  Graphs -> SOLUTION: Find the vertex and intercepts for each parabola, and sketch its graph. y= -x^2 -3x - 2      Log On


   

Question 57696This question is from textbook Elementary and Intermediate Algebra
: Find the vertex and intercepts for each parabola, and sketch its graph.
y= -x^2 -3x - 2 This question is from textbook Elementary and Intermediate Algebra

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertex and intercepts for each parabola, and sketch its graph.
y= -x^2 -3x - 2
Rewrite as :
-(x^2+3x+?=y+2+?
Complete the square to get:
-(x^2+3x+(3/2)^2)=y+2-(3/2)^2
Factor to get:
-(x+(3/2))^2=y-(1/4)
Vertex at (-(3/2),1/4)
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Intercepts:
Y-intercept-----
Let x=0 then y=2
This is the y-intercept.
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x-intercepts---------
Let y=0 then
-x^2-3x-2=0
x^2+3x+2=0
(x+2)(x+1)=0
x=-2 or x=-1
These are the x-intercepts.
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Cheers,
Stan H