Mathematics

Question

determine the equation of the parabola passing through the points (-3,13), (0,1), and (1, -7)​

2 Answer

  • Answer:

    y=-5x+1

    Step-by-step explanation:

    The equation is: y=mx+b

    m = the slope of the line

    b = the y-intercept (0,b)

    The y-intercept is (0,1) so b = (0,1)

    So the equation would be y =mx+1

    Now in order to calculate the slope, the equation is:

    y₂-y₁    over

    x₂-x₁

    So we should use the points (-3,13) and (1,-7).

    -7-13 over (over means a fraction symbol)

    1+3

    Simplify:

    -20 over 4   =-5/1    = -5    

    M=-5

    So the equation is now:

    y=-5x+1

  • Answer:

    Step-by-step explanation:

    You need to do some solving simultaneously to get these values.  Your quadratic equation is of the form

    [tex]ax^2+bx+c=y[/tex]

    Use the coordinates you've been given to solve 3 equations.  It will be super simple if we start with the coordinate (0, 1).  Here's why (obvious after some substitution is done):

    [tex]a(0)^2+b(0)+c=1[/tex] which gives us that

    c = 1.  Now we have a variable to plug in for c to solve for a and b.  Again, we have coordinates that we can use to create 2 more equations:

    [tex]a(-3)^2+b(-3)+1=13[/tex] and, simplified:

    9a - 3b = 12

    and the second equation is:

    [tex]a(1)^2+b(1)+1=-7[/tex] and, simplified:

    a + b = -8

    Now combine the 2 bold equations and solve by elimination or substitution to find either a or b.  I chose elimination and multiplied the second equation by 3 to get a new equation:

    3a + 3b = -24

    Using the elimination method:

    9a - 3b = 12

    3a + 3b = -24

    You can see that the b's subtract each other away, leaving us with

    12a = -12 so

    a = -1

    Now plug -1 in for a to solve for b:

    -1 + b = -8 so

    b = -7 and the quadratic is

    [tex]-x^2-7x+1=y[/tex]

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