A parabola has two x intercepts at (-2 , 0) and (-3 , 0) and passes through the point (5 , 10). Find the equation of this parabola.
+129850 We have that
y = a ( x + 2) ( x + 3)
And since it passes through (5, 10) we can find "a" thusly
10 = a ( 5+2) ( 5 + 3)
10 = a (7)(8)
10 = a (56)
a = ( 10 / 56) = 5 / 28
Then we have that
y = (5/28) ( x + 2) ( x + 3)
y = (5/28) (x^2 + 5x + 6)
y = (5/28)x^2 + (25/28)x + 15/14
