Maths-
General
Easy

Question

Compare each function to f, shown in the table. Which function has lesser minimum value? Explain


h(x) = x2 + x – 3.5

The correct answer is: -3.75


    We have given two functions f(x) and h(x).
    h(x) = x2 + x – 3.5
    For f(x) , minimum value of the function will be the y-coordinate of the given point which has minimum values
    (1,0) , (2,-3) , (3,-4) , (4,-3) (5,0)
    In the given points minimum value of is (3,-4)
    So, the ,minimum value of f(x) is -4.
    In h(x) = x2 + x – 3.5,  a= 1, b= 1, and c = -3.5. So, the equation for the axis of symmetry is given by

    x = −(1)/2(1)

    x = -1/2

    x = -0.5
    The equation of the axis of symmetry for h(x) = x2 + x – 3.5 is x = -0.5.
    The x coordinate of the vertex is the same:

    h =-0.5
    The y coordinate of the vertex is :

    k = f(h)

    k = h2 + h – 3.5

    k = (-0.5)2 + (-0.5) – 3.5

    k = 0.25 – 0.5 – 3.5

    k = -3.75
    Therefore, the vertex is (-0.5 , -3.75)
    The minimum value of g(x) will be the y-coordinate of vertex = -3.75

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