SOLUTION: For the given equation, list the intercepts and test for symmetry y=x^2-x-20 Find the slope‐intercept equation of the line with the following properties: Perpendicular t

Algebra ->  Coordinate-system -> SOLUTION: For the given equation, list the intercepts and test for symmetry y=x^2-x-20 Find the slope‐intercept equation of the line with the following properties: Perpendicular t      Log On


   

Question 678378: For the given equation, list the intercepts and test for symmetry
y=x^2-x-20
Find the slope‐intercept equation of the line with the following properties:
Perpendicular to the line-9x-8y =96; containing the point(-8-8).
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
y = x%5E2-x-20
0 = (x+4)(x-5)
intercepts at x=-4 and x = 5
complete the square to find the vertex and symmetry
y + 20 = x%5E2-x
y + 20 + 1%2F4 = x%5E2-x%2B%281%2F4%29
y + 81%2F4 = %28x-%281%2F2%29%29%5E2
y = %28x-%281%2F2%29%29%5E2+%2B+%28-81%2F4%29
vertex at (1%2F2,-81%2F4) or (.5,-20.25)
line of symmetry x = 1%2F2 or x = .5
...
graph%28300%2C200%2C-5%2C7%2C-25%2C10%2Cx%5E2-x-20%29
...
...
Using -9x-8y=96, the slope intercept form is...
-9x - 96 = 8y
highlight%28y+=+%28-9%2F8%29x+-+12%29
slope is -9%2F8
A perpendicular line will have a negative inverse (reciprocal) slope of 8%2F9.
Using the determined slope and the point, plug into the point-slope formula
y - -8 = 8%2F9(x--8)
y+8 = 8%2F9x + 8%2F9(8)
y = %288%2F9%29x+%2B+%2864%2F9%29+-+8%289%2F9%29
highlight_green%28y+=+%288%2F9%29x+-+8%2F9%29
...
graph%28300%2C200%2C-20%2C5%2C-10%2C5%2C%28-9%2F8%29x-12%2C+%288%2F9%29x-%288%2F9%29%29
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-Reading Boosters
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