SOLUTION: A) find the coordinates of the vertex and the intercepts B) Sketch the graph by hand with at least FIVE points y=8-x-2x^2 I know to rewrite it to y=-2x^2-x=8 and I found

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A) find the coordinates of the vertex and the intercepts B) Sketch the graph by hand with at least FIVE points y=8-x-2x^2 I know to rewrite it to y=-2x^2-x=8 and I found      Log On


   

Question 532173: A) find the coordinates of the vertex and the intercepts
B) Sketch the graph by hand with at least FIVE points
y=8-x-2x^2

I know to rewrite it to y=-2x^2-x=8
and I found the vertex to be -x/2(-2) which is -1/4 and the graph opens downwards?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
y = -2x^2 -x + 8
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To find the zeroes, factor or use the quadratic equation:
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-2x^2 -x + 8 = 0
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B-1x%2B8+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A-2%2A8=65.

Discriminant d=65 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+65+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+65+%29%29%2F2%5C-2+=+-2.26556443707464
x%5B2%5D+=+%28-%28-1%29-sqrt%28+65+%29%29%2F2%5C-2+=+1.76556443707464

Quadratic expression -2x%5E2%2B-1x%2B8 can be factored:
-2x%5E2%2B-1x%2B8+=+-2%28x--2.26556443707464%29%2A%28x-1.76556443707464%29
Again, the answer is: -2.26556443707464, 1.76556443707464. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B-1%2Ax%2B8+%29

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To find the vertex...
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First, find the axis is symmetry = -b/2a = -(-1)/(2*(-2)) = -1/4
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Then substitute that value for 'x' and solve for y
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y = -2(-1/4)^2 -(-1/4) + 8
y = -2(1/16) +1/4 + 8
y = -2/16 + 1/4 + 8
y = -1/8 + 1/4 + 8
y = 1/8 + 8
y = 65/8
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vertex = (-1/4, 65/8)
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+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-2%2Ax%5E2-x%2B8%29+