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wolverine [178]
2 years ago
11

Given the graph, find an equation for the parabola.

Mathematics
1 answer:
Sauron [17]2 years ago
4 0

Answer:

\Large \boxed{\sf \bf \ \ y=\dfrac{1}{16}(a-3)^2-2 \ \  }

Step-by-step explanation:

Hello, please consider the following.

When the parabola equation is like

y=a(x-h)^2+k

The vertex is the point (h,k) and the focus is the point (h, k+1/(4a))

As the vertex is (3,-2) we can say that h = 3 and k = -2.

We need to find a.

The focus  is (3,2) so we can say.

2=-2+\dfrac{1}{4a}\\\\\text{*** We add 2. ***}\\\\\dfrac{1}{4a}=2+2=4\\\\\text{*** We multiply by 4a. ***}\\\\16a=1\\\\\text{*** We divide by 16. ***}\\\\a=\dfrac{1}{16}

So an equation for the parabola is.

\large \boxed{\sf y=\dfrac{1}{16}(a-3)^2-2 }

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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