SOLUTION: Hi. I'm having trouble with this problem. Can you help me? Sketch the graph of the given parabola and state the coordinates of its vertex and its intercepts. y = 2x^2 - 12x +

Algebra ->  Equations -> SOLUTION: Hi. I'm having trouble with this problem. Can you help me? Sketch the graph of the given parabola and state the coordinates of its vertex and its intercepts. y = 2x^2 - 12x +       Log On


   

Question 127715: Hi. I'm having trouble with this problem. Can you help me?
Sketch the graph of the given parabola and state the coordinates of its vertex and its intercepts.
y = 2x^2 - 12x + 18
( , ) (vertex)
y = (y-intercept)
x = (leftmost x-intercept)
x = (rightmost x-intercept)
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Read first the lesson
Shortcut in finding the vertex of any parabola
Ok, done?
Let's start!
y+=+2x%5E2+-+12x+%2B+18
Differentiating,
dy%2Fdx=4x-12
Equating to zero,
4x-12=0
4x=12
x=3
Solving for y,
y+=+2x%5E2+-+12x+%2B+18
y=2%283%29%5E2-12%283%29%2B18
y=18-36%2B18
y=0
y=0 and x=3 So,
The vertex is at (3,0)
Let's check!
Graph:
graph%281000%2C1000%2C-20%2C20%2C-20%2C20%2Cy+=+2x%5E2+-+12x+%2B+18%29
Ok, we're correct!
Proceed,
to find the x-intercepts, let us equate y=0,
so,
+2x%5E2+-+12x+%2B+18=0
x%5E2-6x%2B9=0
Factoring,
%28x-3%29%5E2=0 since this is a perfect square, there is only one x-intercept.
x-3=0
x=3
So,
the x-intercept is at (3,0).
CHECK:
graph%281000%2C1000%2C-20%2C20%2C-20%2C20%2Cy+=+2x%5E2+-+12x+%2B+18%29
Done!
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HyperBrain!