Find the coordinates of the point of intersection of all parabolas that have equation y=x2+px +q with p+q=2020. The point of intersection is

Question

Find the coordinates of the point of intersection of all parabolas that have equation y=x2+px +q with p+q=2020. The point of intersection is​

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Gerda 2 weeks 2021-09-03T17:29:11+00:00 1 Answers 0 views 0

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    2021-09-03T17:30:26+00:00

    Answer:

    (1,2021)

    Step-by-step explanation:

    P and q can vary subject to their sum being 2020.

    Consider one parabola with p1 and q1 and another with p2 and q2.

    y1=(x1)^2+(p1)(x1)+(q1)

    y1=(x2)^2+(p2)(x2)+(q2)

    At their intersection, the x and y coordinates are the same.

    y1=y2=y

    x1=x2=x

    x^2+(p1)x+(q1)=x^2+(p2)x+(q2)

    Solve for x

    x(p1-p2)=q2-q1

    x=(q2-q1)/(p1-p2)

    Use the constraint that p+q=2020 to eliminate p1 and p2.

    p1=2020-q1

    p2=2020-q2

    x=(q2-q1)/(2020-q1-2020+q2)

    x=(q2-q1)/(q2-q1)

    x=1

    Substitute in the equation for y.

    y=1^2+p(1)+q

    y=2021

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