HELP PLEASE! Write a quadratic function that passes through the point (-1,9), has an axis of symmetry of x=-3 and a minimum value of 7.

Question

HELP PLEASE! Write a quadratic function that passes through the point (-1,9), has an axis of symmetry of x=-3 and a minimum value of 7.

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RobertKer 2 months 2021-07-27T17:37:31+00:00 1 Answers 4 views 0

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    2021-07-27T17:38:49+00:00

    Answer:

    y = \frac{1}{2}x^{2} - 3x + 11.5

    Step-by-step explanation:

    Vertex Form of a quadratic equation;

    y = a( x - h )^{2} + k

    Vertex of the parabolas (h, k)

    The vertex of the parabola is either the minimum or maximum of the parabola. The axis of symmetry goes through the x-coordinate of the vertex, hence h = -3. The minimum of the parabola is the y-coordinate of the vertex, so k= 7. Now substitute it into the formula;

    y = a ( x + 3 ) ^{2} + 7

    Now substitute in the given point; ( -1, 9) and solve for a;

    9 = a( (-1 ) + 3)^2 + 7\\9 = a (2)^{2} + 7\\9 = 4a + 7\\-7           -7\\2 = 4a\\\frac{1}{2} = a\\

    Hence the equation in vertex form is;

    y = \frac{1}{2}(x - 3)^{2} + 7

    In standard form it is;

    y = \frac{1}{2}x^{2} - 3x + 11.5

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