Finding X-Axis Intersections: Zero Substitution Method

To solve this problem, we need to determine whether substituting $x = 0$ gives us the points of intersection with the x-axis for the parabola $y = (x - p)^2$.

To find the x-intercepts of any function, we set $y = 0$ because the x-intercepts occur where the curve meets the x-axis, which implies a zero output or function value:

• Start with the equation: $y = (x - p)^2$.
• Set $y = 0$ for the x-intercept: $(x - p)^2 = 0$.
• Solving this gives $(x - p) = 0$, which simplifies to $x = p$.
• Thus, the x-intercept happens at the point where $x = p$, not where $x = 0$.

Therefore, substituting $x = 0$ does not provide the x-intercepts. Instead, it provides the y-intercept. Therefore, the statement given in the problem is False.

Thus, the solution to the problem is False.