Algebra

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Without graphing, describe the end behavior of the graph of f(x) = -5X^2 - 3X + 1

Please explain

  • Algebra -

    it's a parabola opening down.
    End behavior should be clear.

  • Algebra -

    The graph of any function in the form

    y = a x ^ 2 + b x + c is a parabola.

    A quadratic equationhas two solutions.

    In this case :

    x 1 = [ - 3 -s qrt ( 29 ) ] / 10

    and

    x 2 = [ - 3 + sqrt ( 29 ) ] / 10


    If coefficient a is positive then the graph of parabola is concave up.

    If coefficient a is negative then the graph of parabola is concave down.

    In this case a = - 5

    That mean parabola is concave down.


    Parabolas have a highest or a lowest point (depending on whether they open up or down), called the vertex.

    Each parabola has a vertical line of symmetry that passes through its vertex.

    The formula for the x - coordinata of a vertex :

    h = - b / 2 a

    In this case :

    h = - ( - 3 ) / 2 * ( - 5 )

    h = 3 / - 10 = - 3 / 10


    For x = - 3 / 10

    y = - 5 x ^ 2 - 3 x + 1

    y = - 5 * ( 3 / 10 ) ^ 2 - 3 * ( - 3 / 10 ) + 1

    y = - 5 * 9 / 100 + 9 / 10 + 1

    y = - 45 / 100 + 9 / 10 + 1

    y = - 45 / 100 + 90 / 100 + 100 / 100

    y = 145 / 100

    y = 5 * 29/ ( 5 * 20 )

    y = 29 / 20

    Coordinate of vertex ( - 3 / 10 , 29 / 20 )



    P.S.

    If you don't know how to solve quadratic equation in google type:

    quadratic equation online

    When you see list of results click on:

    Free Online Quadratic Equation Solver:Solve by Quadratic Formula

    When page be open in rectangle type:

    -5 x ^ 2 - 3 x + 1 = 0

    and click option: solve it

    You will see solution step-by step


    If you want to see graph of your function in google type:

    function graphs online

    When you see list of results click on:

    rechneronline.de/function-graphs

    When page be open in blue rectacangle type:

    - 5 x ^ 2 - 3 x + 1

    Then click option : Draw

    You will see graph of your function

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