1. For the first graph:
1. Concavity: The parabola opens upwards, so it is concave up.
2. Vertex: The vertex is at the origin, which is the point $(0,0)$.
3. Axis of Symmetry: The axis of symmetry is the vertical line $x=0$ (the y-axis).
4. Maximum/Minimum Value: Since it opens upwards, the vertex is a minimum point with minimum value $0$.
5. x-intercepts: The parabola passes through the origin, so the x-intercept is at $(0,0)$.
6. y-intercepts: The y-intercept is also at $(0,0)$.
7. Domain: The parabola extends infinitely left and right, so the domain is all real numbers: $(-\infty, \infty)$.
8. Range: Since the minimum value is $0$ and it opens upwards, the range is $[0, \infty)$.
2. For the second graph:
1. Concavity: The parabola opens downwards, so it is concave down.
2. Vertex: The vertex is near $(-2, -4)$.
3. Axis of Symmetry: The axis of symmetry is the vertical line $x = -2$.
4. Maximum/Minimum Value: Since it opens downwards, the vertex is a maximum point with maximum value approximately $-4$.
5. x-intercepts: The parabola crosses the x-axis at two points symmetric about $x=-2$; exact values are not given but they exist.
6. y-intercepts: The y-intercept is where the parabola crosses the y-axis; exact value not given but it exists within the range $y \in [-5,5]$.
7. Domain: The parabola extends infinitely left and right, so the domain is all real numbers: $(-\infty, \infty)$.
8. Range: Since the maximum value is approximately $-4$ and it opens downwards, the range is $(-\infty, -4]$.
Graph Properties 765908
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