To solve the equation 2x2 = 2, we can start by simplifying it. First, divide both sides of the equation by 2:
x2 = 1
Next, to find the values of x, we take the square root of both sides:
x = ±1
This means that the solutions to the equation are x = 1 and x = -1.
Now, let’s explore how we can visualize these solutions using a graph of the related function. The function related to the equation is:
f(x) = 2x2
We can graph this function on a coordinate plane. To visualize it:
- First, plot the parabola, which opens upwards since the coefficient of x2 is positive.
- The vertex of the parabola is at the origin (0,0), and it is symmetric around the y-axis.
- Next, notice that the line y = 2 is a horizontal line that intersects the y-axis at (0,2).
The points where the graph of f(x) intersects the line y = 2 are precisely the solutions to the equation 2x2 = 2. From our earlier calculations, we determined that these intersection points occur when:
- x = 1, where f(1) = 2
- x = -1, where f(-1) = 2
Therefore, by graphing the function f(x) = 2x2 and the line y = 2, we can visually confirm that the solutions to the equation 2x2 = 2 are indeed x = 1 and x = -1.