Register to reply

Finding the function of a Parabola

by whitehorsey
Tags: function, parabola
Share this thread:
whitehorsey
#1
Aug7-09, 01:43 AM
P: 192
1. The graph of a quadratic function (a parabola) has x-intercepts -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!
Phys.Org News Partner Science news on Phys.org
Fungus deadly to AIDS patients found to grow on trees
Canola genome sequence reveals evolutionary 'love triangle'
Scientists uncover clues to role of magnetism in iron-based superconductors
Дьявол
#2
Aug7-09, 03:26 AM
P: 365
The parabola has formula y=A(x+B)2+C
You got the intercepts i.e y=0, x1=-1, x2=3

Have you ever learned about Vieta's formulas?

x1+x2=-b/a
x1*x2=c/a

where

x2+(b/a)x+c/a=0

You already got the solutions of the quadratic equation.
Mark44
#3
Aug7-09, 01:28 PM
Mentor
P: 21,258
In general, the graph of a parabola is given by the equation y = ax2 + bx + c, which can also be written as y = a(x - r1)(x - r2). Since you are given the two x-intercepts, you should be able to figure out what r1 and r2 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 x-intercepts, provided that there are two x-intercepts. 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.

whitehorsey
#4
Aug15-09, 05:06 PM
P: 192
Finding the function of a Parabola

Ok Thank You!


Register to reply

Related Discussions
Finding a parabola given two x intercepts Precalculus Mathematics Homework 3
Finding the equation of a parabola General Math 3
Finding equation of a parabola? Help Precalculus Mathematics Homework 4
Finding the equation of a parabola Precalculus Mathematics Homework 3
A parabola delta function Calculus 30