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Find the standard form of the equation

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whose graph has a vertex (-3,4 )and contains the point (-4,7)?

asked Mar 29, 2013 in PRECALCULUS by linda Scholar

1 Answer

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The vertex (h , k) and the point (x , y) then

The standard vertex form : y = a(x - h)2 + k

 For the given problem

The vertex (h , k) is (-3 , 4) and the point (x , y) is (-4 , 7) then

Substitute h = -3 , k = 4 , x = -4 and y = 7 in the standard form of equation y = a(x - h)2 + k

There fore 7 = a(-4 -(-3))2 + 4

7 = a(-4 + 3)2 + 4

7 = a(-1)2 + 4

7 = a + 4

Subtract 4 from each side

7 - 4 = a + 4 - 4

3 = a + 0

3 = a

Recall : symmetric property a = b then b = a

a = 3

Substitute a = 3 , h = -3 and  k = 4 in the standard form of equation : y =a(x - h)2 + k

y = 3(x - (-3))2 + 4

y =3(x + 3)2 + 4

y = 3(x2 + 6x + 9) + 4

y = 3x2 + 18x + 27 + 4

y = 3x2 + 18x + 31

The standard form of the equation : .

graph for y = 3x^2 + 18x + 31

 

answered Apr 3, 2013 by diane Scholar

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