Write the equation of each parabola in vertex form.

Question

Vertex: (-3,7) Point: (-2,-5)

 

Vertex: (4,0) Point: (-6,-3)

Answer 1

Parabola equation in vertex form y = a(x-h)^2+k

Here (h,k) = (-3,7)

y = a(x+3)^2+7

Point (-2,-5) = (x,y)

-5 = a(-2+3)^2+7

-5 = a+7

-5 = a+7

Subtract 7 to each side.

-5-7 = a+7-7

a = -12

Parabola equation in vertex form y = a(x-h)^2+k

y = -12(x+3)^2

y = -12(x^2+9+6x)

y = -12x^2-108-72x

y = -12x^2-72x-108

Answer 2

1) Vertex form of parabola y  = a (x - h ) ²+ k

Where (h ,k ) is the vertex.

Vertex (-3,7) = (h ,k )

y  = a (x - (-3) ) ² + 7

y = a (x + 3)²  + 7 ------> (1)

To find a value

The parabola passes through (-2, -5)

Substitute (x, y) = (-2,-5) in y = a (x + 3)²  + 7

-5 = a (- 2 + 3)²  + 7

-5 = a + 7

a = -12

Substitute the a value in y = a (x + 3)²  + 7.

The parabola is in vertex form y = -12 (x + 3)²  + 7.

2) Vertex (4,0) = (h ,k )

y  = a (x - 4 ) ² + 0

y = a (x - 4)²   ------> (i)

To find a  value

The parabola passes through (-6, -3)

Substitute (x, y) = (-6,-3) in y = a (x - 4)² 

-3 = a (- 6 - 4)² 

-3 = 100a

a = -3/100 = -0.122

Substitute the a value in y = a (x - 4)²  .

The parabola is in vertex form .