lady D realizada en Science & MathematicsMathematics · hace 9 años

can you help me with pre-cal homework?

Find B so that F(x)=-x^2+bx-75 has a maximum value of 25.

help pliz i dont get it :(

1 respuesta

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  • hace 9 años
    Respuesta favorita

    For y = ax² + bx + c there is a turning point corresponding to

    x = -b / 2a

    In the example given we know it is a maximum turning point since coefficient of x² is negative which gives a downward opening parabola.

    In this case max value attained when x = -b/-2 = b/2.

    f(b/2) = -(b/2)² + b(b/2) - 75 = 25

    = -b²/4 + b²/2 - 75 = 25

    b² / 4 - 75 = 25

    b² = 400

    b= -20 and b = 20

    When b = -20 roots are x = -15 , -5

    When b = 20 roots are 5 , 15

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