I have to find the x-intercept.
The equation is y=-2((x-4)^2)+1
I have to factor, but I have no idea how to factor this. I really need help on this, please.
To find the x-intercept of the equation y = -2((x - 4)^2) + 1, you need to find the value(s) of x where y equals zero (because the x-intercept is the point where the graph crosses the x-axis, and at that point, the y-coordinate is zero).
To factor the equation, you need to start by setting y equal to zero and solving for x:
0 = -2((x - 4)^2) + 1
Next, you can isolate the quadratic term on one side of the equation:
2((x - 4)^2) = 1
Now, divide both sides of the equation by 2:
(x - 4)^2 = 1/2
To remove the square, take the square root of both sides:
√[(x - 4)^2] = ±√(1/2)
Simplifying further:
x - 4 = ±√(1/2)
Now, solve for x separately for each term:
x - 4 = √(1/2) or x - 4 = -√(1/2)
For the positive square root:
x = √(1/2) + 4
For the negative square root:
x = -√(1/2) + 4
These are the two potential x-intercepts of the given equation. However, to determine whether they are actual x-intercepts, you can substitute these values back into the original equation and check if y equals zero at those points.