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Finding the function of a Parabola 
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#1
Aug709, 01:43 AM

P: 192

1. The graph of a quadratic function (a parabola) has xintercepts 1 and 3 and a range consisting of all number less than or equal to 4. Determine an expression for the function.
2. none 3. I do not know how to use the intercepts and the range and manipulate it in to a function. Can you show me step by step? Thank You! 


#2
Aug709, 03:26 AM

P: 365

The parabola has formula y=A(x+B)^{2}+C
You got the intercepts i.e y=0, x_{1}=1, x_{2}=3 Have you ever learned about Vieta's formulas? x_{1}+x_{2}=b/a x_{1}*x_{2}=c/a where x^{2}+(b/a)x+c/a=0 You already got the solutions of the quadratic equation. 


#3
Aug709, 01:28 PM

Mentor
P: 21,214

In general, the graph of a parabola is given by the equation y = ax^{2} + bx + c, which can also be written as y = a(x  r_{1})(x  r_{2}). Since you are given the two xintercepts, you should be able to figure out what r_{1} and r_{2} are in the second equation I showed.
So all you need to do is determine that value of a. Since the range is all numbers <= 4, the parabola opens downward. The vertex of a parabola is a point on the parabola that is lower than all others (for a parabola that opens upward) or higher than all others (for one that opens downward). The vertex is always midway between the two xintercepts, provided that there are two xintercepts. With this information you should be able to find the coordinates of the vertex, and from them the value of a in the parabola's equation. 


#4
Aug1509, 05:06 PM

P: 192

Finding the function of a Parabola
Ok Thank You!



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