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    vertex, intercepts and ragne of parabola

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    1. find the intercept, vertex, domain, and range, then graph the parabola
    (1) y = x^2 + 2x - 3
    (2) y = -x^2 -5x - 4
    (3) a = b^2 -6b - 16

    2. graph the parabola, state the domain and range:
    (1) y = 1/3x^2 - 6
    (2) y= -x^2 -1
    (3) y = (x - 2)^2

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    Solution Preview

    Please see the attached file for detailed solutions and graphs.

    These problems I having trouble finding the intercept and vertex and then graph stating domain and range
    y-intercept: substituting to the equation gives:
    So the y-intercept is (0, -3)
    x-intercept: substituting and solving the quadratic equation:

    Therefore, the x-intercepts are (-3, 0) and (1, 0).
    Vertex: by completing the squares:

    The vertex is (-1, -4).
    Domain: for x, there is no restriction, therefore, the domain is .
    Range: The parabola opens up because the coefficient of is 1, which is positive. and the vertex is (-1, -4). The range is then , or .
    The ...

    Solution Summary

    The solution is a detailed guide on the graph of parabola. It explains the steps to find out the vertex, intercepts, domain, and range of the parabola. It also shows how to graph the parabola.