Subjects algebra

Graph Properties 765908

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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 $(-\infty, -4]$.