SOLUTION: Write the equation of a parabola with x-intercepts at (3, 0) and (9, 0) that passes through the point (10,-7)

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Question 1127572: Write the equation of a parabola with x-intercepts at (3, 0) and (9, 0) that passes through the point (10,-7)
Found 3 solutions by josmiceli, greenestamps, josgarithmetic:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
The general formula is:

( 3,0 )
( 9,0 )
( 10,-7 )
------------------------------
( 3,0 )

(1)
-------------------------------
(9,0)

(2)
-------------------------------
( 10,-7 )

(3)
-------------------------------
Multiply both sides of (1) by
and subtract (1) from (2)


--------------------------
Plug this result into (3)
(3)
(3)
(3)
(3)
-------------------------------------
You can plug c and b back into (1) and
find a
Will let you finish



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


Answer the question using the symmetry of the parabola and the vertex form of the equation of a parabola,

where (h,k) is the vertex.

(1) With x-intercepts 3 and 9, the axis of symmetry is x=6, so the equation is of the form



(2) Use one of the x-intercepts and the third point in that equation to find the value of a:
    (9,0)   -->   0 = a(3^2)+k   9a+k =  0
    (10,-7) -->  -7 = a(4^2)+k  16a+k = -7
                             -----------
                                 7a   = -7
                                    a = -1


The equation is now of the form



(3) Use either x-intercept to find k:




We are done....

ANSWER:

Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!




The given point of (10,-7):




-
----------the equation in factored form
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