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Home Q & A Board Science-Related Homework Help Mathematics
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_maddie _maddie
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10 years ago
How do you find an equation of a quadratic that is given the maximum value and the x-intercepts?

and

How would you find the equation of a quadratic that is given the vertex and the x-intercepts?

Thank you!
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wrote...
#1
10 years ago
I am assuming you are an algebra student.

Here is an example. You are looking for the standard form of a quadratic, which is given as:

y = a(x - h) + k

where (x,y) is any point on the graph (use one the intercepts, which will be (x,o) in this simple case) and (h,k) is the vertex. Here is an example.

A parabola, with verical axis, has a vertex at (1 , - 8) and passes through the point (2 , - 6). Find the x intercepts of this parabola.



If h and k are the coordinates of the vertex, the quadratic function in vertex form corresponding to this parabola is given by

f(x) = a (x - h) 2 + k

= a (x - 1) 2 - 8

after plugging in the vertex for h and k.

Next, use the fact that (2 , - 6) is a point on the graph of the parabola to find coefficient a by plugging in 2 and -6 for  x and y:

- 6 = a (2 - 1) 2 - 8

Solve for a to obtain

a = 2

The equation of the parabola is given by

f(x) = 2 (x - 1) 2 - 8
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darkp0tat0darkp0tat0
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10 years ago
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#3
10 years ago
quadratic equation can be solved...
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