# SOLUTION: the graph of a quadratic function (a parabola) has x-intercepts -1 and 3 and a range consisting of all numbers less than or equal to 4. Determine the expression for the function.

Algebra ->  Algebra  -> Equations -> SOLUTION: the graph of a quadratic function (a parabola) has x-intercepts -1 and 3 and a range consisting of all numbers less than or equal to 4. Determine the expression for the function.      Log On

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 Question 206260: the graph of a quadratic function (a parabola) has x-intercepts -1 and 3 and a range consisting of all numbers less than or equal to 4. Determine the expression for the function.Found 2 solutions by Marth, Theo:Answer by Marth(57)   (Show Source): You can put this solution on YOUR website!The base function is "a range consisting of all numbers less than or equal to 4" The parabola must open downwards because of less than or equal. But, has a range of (-infinity, 0]. So you need to shift it up 4. "x-intercepts -1 and 3" The normal x intercepts for would be -2, 2. You need to shift the parabola to the right 1 to get -1, 3. Answer by Theo(3458)   (Show Source): You can put this solution on YOUR website!your x intercepts are -1 and 3 and this is a quadratic equation. ----- this means that (x+1)*(x-3) = 0 because that is the quadratic equation that would yield these 2 x intercepts. ----- multiplying them out we get ----- that's our equation. ----- a limitation is that the range of our function can't be greater than 4. ----- Since y represents the range of our function, this means y has to be less than or equal to 4. ----- since our equation is y = f(x) = , this means that would represent the maximum value that y could be. ----- in order to restrict the range, we have to restrict the domain because the range is dependent on the domain. ----- we need to find the x values for when y = 4 ----- if we subtract 4 from both sides of the equation of we get ----- if we find the roots of this equation, we should be able to find the x values for when y = 4. ----- solving the equation of using the quadratic formula of yields the following answers: ----- x = 3.828427125 or x = -1.828427125 ----- we got this in the following manner: a = 1 b = -2 c = -7 ----- 2a = 2 -b = 2 = = = ----- x = becomes x = which becomes x = 3.828427125 or x = -1.828427125. ----- The graph of our equation is with the restriction that . ----- a graph of our equation would look like this: ----- --- you can see that the lower limit for x will be around -1.828... and the upper limit for x will be around +3.828... and that anything in between is good. ----- those horizontal and vertical lines are just there to let you see the x values and the y values easier. they are not part of the quadratic equation.