3. a) Determine the equation of the parabola, in factored form, y = a(x - r)(x - s)
(7,8)
(-1,0)
(9,0)
b) Express your equation from part a) in standard form, y = ax ^ 2 + bx + c.
a) We can determine the equation of the parabola by using the given points (7,8), (-1,0), and (9,0).
First, set up the equation in factored form: y = a(x - r)(x - s)
Since the parabola passes through the point (7,8), we can substitute these values into the equation:
8 = a(7 - r)(7 - s)
Next, substitute the point (-1,0) into the equation:
0 = a(-1 - r)(-1 - s)
And finally, substitute the point (9,0) into the equation:
0 = a(9 - r)(9 - s)
Now we have a system of three equations that we can solve to find the values of a, r, and s.
b) To express the equation in standard form, y = ax^2 + bx + c, simply expand the factored form equation obtained from part a) and combine like terms. This will give you the standard form of the equation.