Question 284270
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(400,400,-5,5,-10,10,-2x^2 + 4x + 6)}}}


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.