Question

select all of the statements that are true for the given parabola.
a. the minimum is (1, -2)
b. the line of symmetry is y = -2
c. the x - intercepts are (3, 0) and (-1, 0)
d. the maximum is (1, -2)

Explanation:

Step1: Identify vertex

The vertex of an upward - opening parabola is the minimum point. From the graph, the vertex is at the point $(1, - 2)$. So the minimum of the parabola is at $(1,-2)$.

Step2: Determine line of symmetry

For a parabola $y = a(x - h)^2 + k$, the line of symmetry is $x=h$. Since the vertex is $(h,k)=(1, - 2)$, the line of symmetry is $x = 1$, not $y=-2$.

Step3: Find x - intercepts

The x - intercepts are the points where the parabola crosses the x - axis (where $y = 0$). From the graph, the parabola crosses the x - axis at $x=-1$ and $x = 3$, so the x - intercepts are $(-1,0)$ and $(3,0)$.

Step4: Analyze maximum or minimum

Since the parabola opens upward (the graph curves up), it has a minimum, not a maximum.

Answer:

A. The minimum is $(1, - 2)$
C. The x - intercepts are $(3,0)$ and $(-1,0)$