-2x^2+2x=0 parabola

Question

how do you solve this and make graph of the parabola?

Answer 1

Given equation -2x^2+2x = 0

-2x(x-1) = 0

-2x = 0                                       and          x-1 = 0

divide to each side by negitive 2.  and    add 1 to each side.

-2x/-2 = 0/-2                               and       x-1+1 = 0+1

x = 0                                                            x = 1

Solution x = 0,1.

Graph of given parabola

from the graph we can observe the parabola x intercepts are 0,1.

Solution x = 0,1.

Answer 2

• The equation is - 2x² + 2x = 0.

By factor by grouping.

- 2x(x - 1) = 0

Apply zero product property.

- 2x = 0   and      x - 1 = 0

⇒ x = 0   and      x = 1.

The solutions are x = 0 and x = 1.

Note :

The standard form of parabola equation is y = a(x - h)^2 + k, where (h, k) = vertex and axis of symmetry x = h.

• Let, the function y = - 2x² + 2x.

The function represents a parabola.

Write the equation in standard form of a parabola eqaution.

y = - 2x² + 2x

⇒ (- y/2) = x² - x.

To change the expression [x² - x] into a perfect square trinomial add and subtract (half the x coefficient)²

 Here x coefficient = - 1. so, (half the x coefficient)² = (- 1/2)²= 1/4.

- y/2 = x² - x + 1/4 - 1/4

- y/2 = (x - 1/2)² - 1/4

y = - 2(x - 1/2)² + 1/2.

Compare the equation y = - 2(x - 1/2)² + 1/2 with standard form of parabola equation is y = a(x - h)^2 + k, where (h, k) = vertex and axis of symmetry x = h.

Vertex (h, k) = (1/2, 1/2) = (0.5, 0.5), and axis of symmetry x = 1/2 = 0.5.

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 = - 2x2 + 2x	(x, y)
- 0.5	y = -2(-0.5)2+2(-0.5) = -1.5	(- 0.5, -1.5)
0	y = -2(0)2+2(0) = 0	(0, 0)
0.5	y = -2(0.5)2+2(0.5) = 0.5	(0.5, 0.5)
1	y = -2(1)2+2(1) = 0	(1, 0)
1.5	y = -2(1.5)2+2(1.5) = -1.5	(1.5, - 1.5)

1.Draw a coordinate plane.

2.Plot the coordinate points.

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