Two quadratic functions are shown. Function 1: f(x) = 3×2 + 6x + 7 Function 2:<

Question

Two quadratic functions are shown.

Function 1:

f(x) = 3×2 + 6x + 7

Function 2:
x g(x)
−2 13
−1 7
0 3
1 7

Which function has the least minimum value and what are its coordinates? (5 points)

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4 weeks 2021-12-27T13:16:16+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-12-27T13:18:11+00:00

    Answer: the function that has the smaller minimum is g(x), and the cordinates are (0,3)

    Step-by-step explanation:

    We have a function for f(x) and a table for g(x)

    first, quadratic functions are symmetrical.

    This means that if the minimum/maximum is located at x = x0, we will have that:

    f(x0 + A) = f(x0 – A)

    For any real value of A.

    Then when we look at the table, we can see that:

    g(-1) = 7

    g(0) = 3

    g(1) = 7

    then the minimum of g(x) must be at x = 0, and we can see that the minimum value of g(x) is 3.

    Now let’s analyze f(x).

    When we have a quadratic equation of the shape.

    y = a*x^2 + b*x + c

    the minimum/maximum will be located at:

    x = -b/2a

    In our function we have:

    a = 3

    b = 6

    then the minimum is at:

    X = -6/2*3 = -1

    f(-1) = 3*(-1)^2 + 6*-1 + 7 = 3 – 6 + 7 = 3 + 1 = 4

    Then the function that has the smaller minimum is g(x), and the cordinates are (0,3)

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