Question

question 4 of 31 select all of the statements that are true for the given parabola. a. the maximum is (1, -5) b. the minimum is (1, -5) c. the x - intercepts are (0, 3) and (0, -1) d. the line of symmetry is x = 1

Explanation:

Step1: Analyze the parabola's orientation

The parabola opens upwards, so it has a minimum - point and no maximum - point.

Step2: Identify the vertex

The vertex of the parabola is the lowest point. From the graph, the vertex is at the point $(1, - 5)$. So the minimum is $(1, - 5)$.

Step3: Check the x - intercepts

The x - intercepts are the points where the parabola crosses the x - axis. The x - intercepts are the points where $y = 0$. From the graph, the x - intercepts are not $(0,3)$ and $(0, - 1)$ (x - intercepts have $y = 0$, and the given points have $x = 0$ which are y - intercepts). The correct way to find x - intercepts is to set $y=0$ in the parabola's equation. But from the graph, we can see the x - intercepts are not as given.

Step4: Determine the line of symmetry

For a parabola in the form $y=a(x - h)^2 + k$, the line of symmetry is $x = h$. Since the vertex is $(h,k)=(1, - 5)$, the line of symmetry is $x = 1$.

Answer:

B. The minimum is $(1, - 5)$
D. The line of symmetry is $x = 1$