Use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function.

Question

Use the vertex
(h, k)
and a point on the graph
(x, y)

to find the general form of the equation of the quadratic function.
(h, k) = (−6, 2), (x, y) = (3, 8)

Answer 1

Vertex form of a quadratic

 

y = a(x - h)² + k

 

 

Now we just plug in the values to find what "a" is.

 

8 = a(3 + 6)² + 2

 

8 = 81a + 2

 

6 = 81a

 

6/81 = a

 

2/27 = a

 

Then your equation is

 

y = (2/27)(x + 6)² + 2

 

y = (2/27)(x² + 12x + 36) + 2

 

y = (2/27)x² + (8/9)x + (14/3)

Answer 2

y = a(x-h)² + k

y = a(x-(-6))² + 2

y = a(x+6)² + 2

 

Use the given point (3,8) to find the value of a:

y = a(x+6)² + 2

8 = a(3+6)² + 2

8 = a·9² + 2

8 = a·81 + 2

6 = a·81

6/81 = 2/27 = a

 

y = (2/27)(x+6)² + 2

 

Multiply it out to put it into standard form.