Question

Consider the quadratic function y = (x – 2)2 + 5.

Which statements are true about the function and its graph? Select two options.

The vertex of the function is (–2, 5).
There are no real roots for the function.
The graph of the function opens down.
The graph contains the point (2, 5).
The graph intersects the x-axis at one unique point.

Answer 1

Correct choices:
- There are no real roots for the function.
- The graph contains the point (2, 5).

Reason: y = (x − 2)^2 + 5 has vertex (2, 5) and since (x − 2)^2 ≥ 0, y ≥ 5, so it never reaches 0 (no x-intercepts). The coefficient of (x − 2)^2 is positive, so the parabola opens up, not down.