The vertex of this parabola is at (-2,-3). When the y-value is -2, the x-value is -5. What is the coefficient of the squared term in the par

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The vertex of this parabola is at (-2,-3). When the y-value is -2, the x-value is -5. What is the coefficient of the squared term in the parabola’s equation? 5 re (-2, -3)​

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Farah 1 month 2021-08-12T07:50:31+00:00 1 Answers 4 views 0

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    2021-08-12T07:51:40+00:00

    Answer:

    The coefficient of the squared term of the equation is 1/9.

    Step-by-step explanation:

    We are given that the vertex of the parabola is at (-2, -3). We also know that when the y-value is -2, the x-value is -5. Using this information we want to find the cofficient of the squared term in the parabola’s equation.

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

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

    Where a is the leading coefficient and (h, k) is the vertex.

    Since the vertex is (-2, -3), h = -2 and k = -3:

    \displaystyle y=a(x-(-2))^2+(-3)

    Simplify:

    y=a(x+2)^2-3

    We are also given that y = -2 when x = -5. Substitute:

    (-2)=a(-5+2)^2-3

    Solve for a. Simplify:

    \displaystyle \begin{aligned} -2&=a(-3)^2-3\\ 1&=9a \\a&=\frac{1}{9}\end{aligned}

    Therefore, our full vertex equation is:

    \displaystyle y=\frac{1}{9}(x+2)^2-3

    We can expand:

    \displaystyle y=\frac{1}{9}(x^2+4x+4)-3

    Simplify:

    \displaystyle y=\frac{1}{9}x^2+\frac{4}{9}x-\frac{23}{9}

    The coefficient of the squared term of the equation is 1/9.

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