Find the x-intercepts. y=x^2-4x+4. Thanks for helping. All of this Algebra has lost me.
To find the x-intercepts of a quadratic equation, we need to determine the values of x for which the equation equals zero. In your case, the equation is y = x^2 - 4x + 4.
To find the x-intercepts, we set y to zero and solve for x. So, we substitute y with zero in the equation:
0 = x^2 - 4x + 4
Now, we can solve this quadratic equation. There are several methods to do this, but one common method is factoring. However, in this case, the equation cannot be factored easily.
Instead, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
Where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In our equation, a = 1, b = -4, and c = 4. Plugging these values into the quadratic formula, we have:
x = (-(-4) ± √((-4)^2 - 4(1)(4))) / (2(1))
Simplifying further gives us:
x = (4 ± √(16 - 16)) / 2
x = (4 ± √0) / 2
x = (4 ± 0) / 2
x = 4 / 2
So, the x-intercept of the given quadratic equation is x = 2.
Therefore, the solution is that the graph of the equation y = x^2 - 4x + 4 has a single x-intercept at x = 2.