Question

1.1 identify the key features of the graph. y - intercept: x - intercepts: axis of symmetry: relative max. relative min. end behavior:

Explanation:

Step1: Find y - intercept

Set $x = 0$ on the graph. The curve intersects the y - axis at $y=0$. So the y - intercept is $0$.

Step2: Find x - intercepts

The graph intersects the x - axis at $x = 0$ and another positive x - value. Let's assume the non - zero x - intercept is $a>0$. So the x - intercepts are $x = 0$ and $x=a$.

Step3: Determine axis of symmetry

Since the graph is a parabola opening to the right (a type of quadratic - like curve in this orientation), there is no axis of symmetry parallel to the coordinate axes in the traditional sense for a function (as it fails the vertical line test). But if we consider the symmetry of the parabolic shape, for a parabola of the form $x=ay^{2}+by + c$, the axis of symmetry is a horizontal line. By observing the graph, we can see that there is no such simple symmetry about a horizontal or vertical line. So, no axis of symmetry.

Step4: Find relative max/min

The graph has a relative minimum at the vertex. The vertex is at the origin $(0,0)$. There is no relative maximum as the graph extends infinitely in the positive x - direction. So relative minimum at $(0,0)$, no relative maximum.

Step5: Determine end - behavior

As $y\to+\infty$, $x\to+\infty$ and as $y\to-\infty$, $x\to+\infty$.

Answer:

y - intercept: $0$
x - intercepts: $0$ and a positive value (assume $a$)
axis of symmetry: None
relative max: None
relative min: $(0,0)$
end - behavior: As $y\to\pm\infty$, $x\to+\infty$