Express each of the following quadratic functions in the form of f(x) = a (x – h)²+ k.Then,state the minimum or maximum value,axis of symmet

Question

Express each of the following quadratic functions in the form of f(x) = a (x – h)²+ k.Then,state the minimum or maximum value,axis of symmetry and minimum or maximum point. (a) f(x) = -2x² + 7x + 4.
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Latifah 5 months 2021-08-04T12:11:19+00:00 1 Answers 6 views 0

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    2021-08-04T12:13:18+00:00

    Given:

    The function is:

    f(x)=-2x^2+7x+4

    To find:

    Express the quadratic equation in the form of f(x)=a(x-h)^2+k, then state the minimum or maximum value,axis of symmetry and minimum or maximum point.

    Solution:

    The vertex form of a quadratic function is:

    f(x)=a(x-h)^2+k              …(i)

    Where, a is a constant, (h,k) is the vertex and x=h is the axis of symmetry.

    We have,

    f(x)=-2x^2+7x+4

    It can be written as:

    f(x)=-2\left(x^2-3.5x\right)+4

    Adding and subtracting square of half of coefficient of x inside the parenthesis, we get

    f(x)=-2\left(x^2-3.5x+(\dfrac{3.5}{2})^2-(\dfrac{3.5}{2})^2\right)+4

    f(x)=-2\left(x^2-3.5x+(1.75)^2\right)-2\left(-(1.75)^2\right)+4

    f(x)=-2\left(x-1.75\right)^2+2(3.0625)+4

    f(x)=-2\left(x-1.75\right)^2+6.125+4

    f(x)=-2\left(x-1.75\right)^2+10.125                …(ii)

    On comparing (i) and (ii), we get

    a=-2,h=1.75,k=10.125

    Here, a is negative, the given function represents a downward parabola and its vertex is the point of maxima.

    Maximum value = 10.125

    Axis of symmetry : x=1.75

    Maximum point = (1.75,10.125)

    Therefore, the vertex form of the given function is f(x)=-2\left(x-1.75\right)^2+10.125, the maximum value is 10.125, the axis of symmetry is x=1.75 and the maximum point is (1.75,10.125).

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )