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shusha [124]
3 years ago
15

The graph of a function is a parabola that has a minimum at the point (-3,9). Which equation could represent the function?

Mathematics
1 answer:
Masteriza [31]3 years ago
5 0

Well there are no choices listed so it's going to be hard to say which; we'll write an expression for all of them and then give a few instances.

A parabola with a minimum forms a CUP, concave-up positive, meaning the coefficient a on x² must be positive, a>0.  

The general form with vertex (p,q) is

y = a(x-p)² + q

So for us, all our parabolas are of the form

y = a(x- -3)² + 9

y = a(x² + 6x + 9) + 9

y = ax² + 6ax + 9(a+1)

That's the general form for a parabola with vertex (-3,9); a>0 assure the parabola has a minimum at the vertex.

Some instances:

a=1 gives

Answer: y = x²+6x+18

a=4 gives

y = 4x² + 24x + 45

Other positive <em>a</em>s give other possible answers; without the choices it's impossible to know which one they're seeking.

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Step-by-step explanation:

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