SOLUTION: The dimensions of the facade of the house, should be 7m wide and 4 ms high, it should be a parabola, use the origin of the parabola as one corner. Find the quadratic equation to th

Question 956147: The dimensions of the facade of the house, should be 7m wide and 4 ms high, it should be a parabola, use the origin of the parabola as one corner. Find the quadratic equation to that.
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3 points are (0,0), (3.5,4) and (7,0)
y = ax^2 + bx + c
At x = 0, y = 0 --> c = 0
----
At x = 7, y = 0
49a + 7b = 0
7a + b = 0
b = -7a
---
At x = 3.5, y = 4
12.25a + 3.5b = 4
Sub for b
12.25a - 24.5a = 4
-12.25a = 4
a = -16/49
---
b = 16/7
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And then they got
y=16x^2/49+16x/7
What I am wondering is how you got there, because I have looked very hard a it and can not make sense of it, would someone please explain the process a bit more clearly?
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

you are given 3 points which are: (,), (,) and (,)
you need a quadratic equation of a parabola which contain given points
so, use point (,)=> means and

------eq.1
=>
so, we now that our equation will be and we need to find and
now use (,)
,

------eq.2.......solve for

.........eq a1
now, we can use (,)

.....solve for

...........eq a2

use eq a1 and eq a2, make right sides equal
....solve for .......both sides multiply by

now find ...........eq a2

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