SOLUTION: hi i need help with this problem for college algebra. write the equation of the parabola that has x-intercepts (-1,0) and (3,0) and y-intercept (0,6)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: hi i need help with this problem for college algebra. write the equation of the parabola that has x-intercepts (-1,0) and (3,0) and y-intercept (0,6)      Log On


   

Question 284270: hi i need help with this problem for college algebra.
write the equation of the parabola that has x-intercepts (-1,0) and (3,0) and y-intercept (0,6)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
y-intercept of (0,6) means that y is equal to 6 when x is equal to 0.

The constant in the equation therefore needs to be 6.

general form of the equation is ax^2 + bx + c = 0

with c = 6, general form becomes ax^2 + bx + 6 = 0

x-intercepts of (-1,0) and (3,0) are the roots of the equation.

this means that the roots are x = -1 and x = 3.

this means that x+1 = 0 and x-3 = 0.

this means that your equation is (x+1) * (x-3) = 0.

multiply those factors out and you get:

x^2 - 2x - 3 = 0

but c in the equation needed to be 6.

multiply both sides of your equation by -2 to get:

-2x^2 + 4x + 6 = 0

that should be your equation.

a graph of that equation looks like this:

graph%28400%2C400%2C-5%2C5%2C-10%2C10%2C-2x%5E2+%2B+4x+%2B+6%29

The graph looks good.

The y-intercept is 6 as it should be.

The roots of the equation are -1 and 3 as they should be.