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# Standard Form of a Quadratic Equation

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When a quadratic equation is in the form  f(x)  =  a(x - h)2 + k ,  the vertex is  (h, k)

For this problem, they tell us the vertex is  (-1, 5) , so we know that

f(x)  =  a(x - -1)2 + 5

f(x)  =  a(x + 1)2 + 5

We know it goes through the point  (2, -13) , which means  f(2) = -13

f(2)  =  a(2 + 1)2 + 5       And  f(2) = -13

-13  =  a(2 + 1)2 + 5

-13  =  9a + 5

-18  =  9a

-2  =  a

Now we've found  a  , so we know that

f(x)  =  -2(x + 1)2 + 5            And here's a graph to check it.

hectictar  Oct 23, 2017
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#1
+6943
+1

When a quadratic equation is in the form  f(x)  =  a(x - h)2 + k ,  the vertex is  (h, k)

For this problem, they tell us the vertex is  (-1, 5) , so we know that

f(x)  =  a(x - -1)2 + 5

f(x)  =  a(x + 1)2 + 5

We know it goes through the point  (2, -13) , which means  f(2) = -13

f(2)  =  a(2 + 1)2 + 5       And  f(2) = -13

-13  =  a(2 + 1)2 + 5

-13  =  9a + 5

-18  =  9a

-2  =  a

Now we've found  a  , so we know that

f(x)  =  -2(x + 1)2 + 5            And here's a graph to check it.

hectictar  Oct 23, 2017

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