the vertex of this parabola is at (2,-4). when the y-value us -3, the x-value is -3. what is the coefficient of the squared term in the para

Question

the vertex of this parabola is at (2,-4). when the y-value us -3, the x-value is -3. what is the coefficient of the squared term in the parabolas equation?​

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Vân Khánh 3 years 2021-07-18T22:47:19+00:00 2 Answers 29 views 0

Answers ( )

  1. Nick
    0
    2021-07-18T22:48:33+00:00
    Reply

    Answer:

    -5

    Step-by-step explanation:

    from a p e x

  2. minhkhue
    0
    2021-07-18T22:48:50+00:00
    Reply

    Answer:

    The coefficient of the squared term is 1/25.

    Step-by-step explanation:

    We are given that the vertex of a parabola is at (2, -4). We also know that y = -3 when x = -3.

    And we want to determine the coefficient of the squared term of the equation.

    Since we are given the vertex, we can use the vertex form of the quadratic:

    \displaystyle y = a(x-h)^2+k

    Where (h, k) is the vertex and a is the leading coefficient. The leading coefficient is also the coefficient of the squared term, so we simply need to find the value of a.

    Since the vertex is at (2, -4), h = 2 and k = -4. Substitute:

    \displaystyle y = a(x-2)^2-4

    y = -3 when x = -3. Solve for a:

    \displaystyle (-3) = a((-3)-2)^2-4

    Simplify:

    \displaystyle 1 = a(-5)^2\Rightarrow a = \frac{1}{25}

    Therefore, our function in vertex form is:

    \displaystyle f(x) = \frac{1}{25}\left(x-2)^2-4

    Hence, the coefficient of the squared term is 1/25.

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