Complete the table of values for y=2x squared + x

y=2x^2 + 2x - 3 x -2 -1 0 1 2

Step By Step Explanation:

The values can be find by plugging the x values in the equation which gives us the y value ,

x -2 -1 0 1 2

y 1 -3 -3 1 9

(b) Plot the points on the graph and join by a smooth curve.

(c) The line y=1 will be passing through 1 and parallel to x-axis.

(d) solve 2x^2 + 2x - 3 = 1

Subtract 1 from both the sides ,

2x^2 + 2x - 2 = 0

Factoring out the 2 from the equation ,

2(x^2 + x - 1) = 0

x^2 + x - 1 = 0

Apply the quadratic formula

x=(-1-sqrt(5))/2 and x = (-1+sqrt(5))/5

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it