Find the standard form of the equation

Question

 

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

Answer 1

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 : .