Explain how to write a quadratic equation given the following three points on the graph (5,31) (3,11) (0,11)

Question

Explain how to write a quadratic equation given the following three points on the graph (5,31) (3,11) (0,11)

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Philomena 7 months 2021-07-17T07:18:13+00:00 1 Answers 9 views 0

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    2021-07-17T07:19:27+00:00

    Given:

    The graph of a quadratic function passes through the points (5,31) (3,11) (0,11).

    To find:

    The equation of the quadratic function.

    Solution:

    A quadratic function is defined as:

    y=ax^2+bx+c            …(i)

    It is passes through the point (0,11). So, substitute x=0,y=11 in (i).

    11=a(0)^2+b(0)+c

    11=c

    Putting c=11 in (i), we get

    y=ax^2+bx+11               …(ii)

    The quadratic function passes through the point (5,31). So, substitute x=5,y=31 in (ii).

    31=a(5)^2+b(5)+11

    31-11=a(25)+5b

    20=25a+5b

    Divide both sides by 5.

    4=5a+b                  …(iii)

    The quadratic function passes through the point (3,11). So, substitute x=3,y=11 in (ii).

    11=a(3)^2+b(3)+11

    11-11=a(9)+3b

    0=9a+3b

    Divide both sides by 3.

    0=3a+b                 …(iv)

    Subtracting (iv) from (iii), we get

    4-0=5a+b-3a-b

    4=2a

    \dfrac{4}{2}=a

    2=a

    Putting a=2 in (iv), we get

    0=3(2)+b

    0=6+b

    -6=b

    Putting a=2,b=-6 in (ii), we get

    y=(2)x^2+(-6)x+11

    y=2x^2-6x+11

    Therefore, the required quadratic equation is y=2x^2-6x+11.

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