SOLUTION: find the x-intercepts of the parabola with (4,75) and y-intercept (0,27)

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Question 310267: find the x-intercepts of the parabola with (4,75) and y-intercept (0,27)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The general equation for a parabola is
y=ax%5E2%2Bbx%2Bc
From the point (4,75),
75=a%2816%29%2Bb%284%29%2Bc
1.16a%2B4b%2Bc=75
From the intercept (0,27),
27=a%280%29%2Bb%280%29%2Bc
2.c=27
Then eq. 1 becomes,
16a%2B4b%2B27=75
16a%2B4b=48
4a%2Bb=12
At this point, you have two equations with three unknowns.
You can solve in terms of one of the unknowns.
You can find b in terms of a, this way your solution is based on the value of a.
b=12-4a and the general equation becomes,
y=ax%5E2%2B%2812-4a%29x%2B27
You can find the roots using the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28%284a-12%29+%2B-+sqrt%28+%2812-4a%29%5E2-4%2Aa%2A27+%29%29%2F%282%2Aa%29+
x+=+%28%284a-12%29+%2B-+sqrt%28+%28144-96a%2B16a%5E2%29-108a%29%29%2F%282%2Aa%29+
x+=+%28%284a-12%29+%2B-+sqrt%28+16a%5E2%2B204a%2B144%29%29%2F%282%2Aa%29+
x+=+%28%284a-12%29+%2B-+sqrt%28+%284a-3%29%284a-12%29+%29%29%2F%282%2Aa%29+
Can't simplify any more than that.