SOLUTION: Find the vertex, x-intercept(s), and y-intercept of the parabola given by y=7x^2+21x-378. If the parabola does not have any x-intercepts, enter NONE for both coordinates of both in

Algebra ->  Radicals -> SOLUTION: Find the vertex, x-intercept(s), and y-intercept of the parabola given by y=7x^2+21x-378. If the parabola does not have any x-intercepts, enter NONE for both coordinates of both in      Log On


   

Question 362085: Find the vertex, x-intercept(s), and y-intercept of the parabola given by y=7x^2+21x-378. If the parabola does not have any x-intercepts, enter NONE for both coordinates of both intercepts. If it has exactly one x-intercept, enter it as the first intercept and enter NONE for both coordinates of the second intercept. If it has two x-intercepts list them in increasing order.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Convert to vertex form by completing the square.
y=7x%5E2%2B21x-378
y=7%28x%5E2%2B3x%29-378
y=7%28x%5E2%2B3x%2B9%2F4%29-378-7%289%2F4%29
y=7%28x%2B3%2F2%29%5E2-1512%2F4-63%2F4
y=7%28x%2B3%2F2%29%5E2-1575%2F4
The vertex is (-3%2F2,-1575%2F4).
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To find the y-intercept, set x=0 and solve for y.
y=7x%5E2%2B21x-378
y=7%280%29%2B21%280%29-378
y=-378
(0,-378)
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To find the x-intercept, set y=0 and solve for x.
y=7%28x%2B3%2F2%29%5E2-1575%2F4
7%28x%2B3%2F2%29%5E2-1575%2F4=0
7%28x%2B3%2F2%29%5E2=1575%2F4
%28x%2B3%2F2%29%5E2=225%2F4
x%2B3%2F2=0+%2B-+15%2F2
x=-3%2F2+%2B-+15%2F2
x%5B1%5D=12%2F2=6
x%5B2%5D=-18%2F2=-9
(6,0)
(-9,0)
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