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Find the equation of the quadratic function whose graph is a parabola containing the points(0 ​,4)(3 ​,19) and(4,68) .

 Mar 7, 2021
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ax^2 + bx + c = y       when x = 0       c = 4   (given as the first point)

ax^2 + bx + 4 = y     sub in    3,19

9a + 3b + 4 = 19              and sub in 4, 68

16a + 4b + 4 = 68          now you have two equations and two unknowns  ....do you know how to solve these?

                                          various ways   ..... multiply first equation by - 1 1/3

-12a -4b - 16/3 =  -76/3       add this to the second equation

4a           -4/3 = 128/3

4a = 132/3

a = 11                     then b = -28

 

 

11 x^2     - 28x   +4    = f(x)  

 

Here is a graph:

https://www.desmos.com/calculator/bdjis3s6tt

 Mar 7, 2021
edited by ElectricPavlov  Mar 7, 2021
edited by ElectricPavlov  Mar 7, 2021

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