a)
x - intercepts: 2 and -1/2
Point = (3, -14)
quadratic formula:
y = a(x -2)(x + 1/2)
we need to solve for a.
-14 = a(3 - 2)(3 + 1/2)
-14 = a(7/2)
a = - 4
so:
y = -4(x -2)(x + 1/2)
y = -4x^2 + 6x + 4
b)
x - intercept = -2 = (-2, 0)
point: (-1, 4)
We can plug both points into two separated equations, as follows:
4 = a(-1)^2 + b(-1) + c (EQUATION 1.)
0 = a(-2)^2 + b(-2) + c (I'll multiply this equation by -1 in order to add the 2 equations together and get rid of c)
4 = a - b + c
0 = -4a + 2b - c
_____________
4 = -3a + b
a = 1/3b - 4/3**
Now we plug back in to the first equation to find c.
4 = 1/3b - 4/3 - b + c
c = 2/3b + 16/3 **
Now we plug one last time on the equation 1 with all b variables:
4 = 1/3b - 4/3 - b + 2/3b + 16/3
b =