1. find the vertex of the parabola whose equation is y = x^2 + 6x + 2.

2. what is the line of symmetry for the parabola whose equation is y = 3x^2 + 24x - 1?

3. what is the line of symmetry for the parabola whose equation is y = x^2 + 10x + 25?

4. find the vertex of the parabola whose equation is y = -2x^2 + 8x - 5.

5. what is the line of symmetry for the parabola whose equation is y = x^2 - 12x + 7?

6. find the vertex of the parabola whose equation is y = x^2 - 4x + 6.

1. y = x^2 + 6x + 2 = x^2 + 6x + 9 - 7 = (x + 3)^2 - 7
The vertex of the parabola whose equation is y = x^2 + 6x + 2 is (-3, -7).

2. y = 3x^2 + 24x - 1 = 3(x^2 + 8x) - 1 = 3(x^2 + 8x + 16) - 1 - 48 = 3(x + 4)^2 - 49
The line of symmetry for the parabola whose equation is y = 3x^2 + 24x - 1 is x = -4

3. y = x^2 + 10x + 25 = (x + 5)^2
The line of symmetry for the parabola whose equation is y = x^2 + 10x + 25 is x = -5

4. y = -2x^2 + 8x - 5 = -2(x^2 - 4x) - 5 = -2(x^2 - 4x + 4) - 5 + 8 = -2(x - 2)^2 + 3
The vertex of the parabola whose equation is y = -2x^2 + 8x - 5 is (2, 3).

5. y = x^2 - 12x + 7 = x^2 - 12x + 36 - 29 = (x - 6)^2 - 29
The line of symmetry for the parabola whose equation is y = x^2 - 12x + 7 is x = 6

6. y = x^2 - 4x + 6 = x^2 - 4x + 4 + 2 = (x - 2)^2 + 2
The vertex of the parabola whose equation is y = x^2 - 4x + 6 is (2, 2).

Answer with explanation:

We know that for any parabola equation of the type:

The vertex of the parabola is given by:

(h,k)

where,

and the line of symmetry of the parabola is:

Ques 1)

We have the parabola equation as:

i.e.

Hence,

and

Hence, Vertex=(-3,-7)

and axis of symmetry is: x= -3

Ques 2)

We have:

a=3, b=24 and c=-1

Hence,

and,

Hence, Vertex=( -4,-49)

and Axis of symmetry is: x= -4

Ques 3)

Hence,

and,

Hence, Vertex=( -5,0)

and Axis of symmetry is: x= -5

Ques 4)

We have:

Hence,

and,

Hence, Vertex=( 2,3)

and Axis of symmetry is: x= 2

Ques 5)

We have:

Hence,

and,

Hence, Vertex=(6,-29)

and Axis of symmetry is: x= 6

Ques 6)

We have:

Hence,

and,

Hence, Vertex=(2,2)

and Axis of symmetry is: x= 2