Find the vertex of f(x) = 3(x-7)(x+5) Please show your work. ^^ I’ve been having a bit of trouble with this question :( a

Question

Find the vertex of f(x) = 3(x-7)(x+5)
Please show your work.

^^ I’ve been having a bit of trouble with this question 🙁 although it’s simple quadratics is not my strong suit

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Mít Mít 2 months 2021-07-23T08:56:06+00:00 2 Answers 6 views 0

Answers ( )

    0
    2021-07-23T08:57:25+00:00

    Answer:

    vertex (1, -108)

    Step-by-step explanation:

    First find the zeros

    f(x) = 3(x-7)(x+5)

    0 =  3(x-7)(x+5)

    Using the zero product property

    x-7 = 0   x+5 = 0

    x = 7  x = -5

    The x coordinate of the vertex is the average of the zeros

    (7+-5)/2 = 2/2 =1

    To find the y coordinate, substitute the x coordinate into the equation

    y = 3(1-7)(1+5) = 3(-6)(6) = -108

    0
    2021-07-23T08:57:35+00:00

    Answer:

    The vertex is at (1, -108).

    Step-by-step explanation:

    We have the function:

    f(x)=3(x-7)(x+5)

    And we want to find its vertex point.

    Note that this is in factored form. Hence, our roots/zeros are x = 7 and x = -5.

    Since a parabola is symmetric along its vertex, the x-coordinate of the vertex is halfway between the two zeros. Hence:

    \displaystyle x=\frac{7+(-5)}{2}=\frac{2}{2}=1

    To find the y-coordinate, substitute this back into the function. Hence:

    f(1)=3((1)-7)((1)+5)=3(-6)(6)=-108

    Therefore, our vertex is at (1, -108).

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