Algebra Help ASAP?

Question

Couple of questions need help ASAP 
1. Write an equation with the line crossing the following two points. (2,-8) (-1,-2) 
2. What are the midpoint and distance between the previous points in question 1? 
3. Convert the following to vertex form and plot. 2xsquared +8x =-11 
4. COMBINE 3radical12 + 6radical48 
5. simplify (long division maybe..) 2xcubed + 11xsquared +13x +4 divided by x+4 

PLEASE HELP!!! Thanks

Answer 1

1) The coordinates are

Slope of the the line  crossing above points is

Point slope form of a line is

Required line equation  is  .

2)

Coordinates of mid point is

Distance between two points is

4) 

.

Answer 2

3)  2x ² + 8x = -11

2x ² + 8x + 11 = 0

The parabola standard form is y = ax ² + bx + c

Now the equation y = 2x ² + 8x + 11

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

Here x ² coefficient is 2, for perfect square make x ² coefficient 1 by dividing each side by 2.

y  = 2x ² + 8x + 11

y /2 = x ² + 4x + 11/2

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

x  coefficient = 4 then (half the x coefficient)² is (2) ² = 4.

So, add 4 to each side.

y /2 + 4 = x ²+ 4x + 11/2 + 4

y /2 + 4 = x ² + 4x + 4 + 11/2

y /2 + 4 = (x + 2) ² + 11/2

y /2 = (x + 2) ² +11/2 - 4

y /2 = (x + 2) ² + 3/2

y  = 2(x + 2)² + 3.

Therefore, vertex form of the parabola is  y  = a  (x - h ) ² + k.

y = 2[x - (-2)] ² + 3

a  = 2 , (h ,k ) = (-2 , 3).

Graph

 y = 2x ² + 8x + 11

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

x	y = 2x 2 + 8x + 11	(x, y )
- 1	y = 2(- 1)^2 +8 (- 1) +11 = 5	(- 1, 5)
- 2	y = 2(- 2)^2 +8 (- 2) +11 = 3	(- 2, 3)
0	y = 2(0)^2 +8 (0) +11 = 11	(0, 11)
-3	y = 2(-3)^2 +8 (-3) +11 = 5	(-3, 5)
-4	y = 2(-4)^2 +8 (-4) +11 = 11	(-4, 11)

1.Draw a coordinate plane.

2.Plot the coordinate points found in the table.

3.Then sketch the graph, connecting the points with a smooth curve.

 

Answer 3

5) Divisior is x + 4 , divident is 2x ³ + 11x ² +13x + 4 

Long division

x + 4    )            2x ³ + 11x ² +13x + 4          ( 2x ² + 3x + 1

                        2x ³ + 8x ²

                      (-)      (-)

                 ________________________

                            3x ²  + 13x

                            3x ²  + 12x

                        (-)      (-)

             _____________________________

                                x  +  4

                                x  +  4

                            (-)    (-)

             _________________________________

                                  0

(2x ³ + 11x ² +13x + 4)/(x + 4) = 2x ² + 3x + 1.