Question

Someone help me please!!!!!!!!!!!

Answer 1

You have 3 unknowns: a, b, and c.  That means you have to have 3 equations to solve for the values of them.  3 unknowns needs 3 different equations.  We will use the first 3 points in the table and thank God that one of them has an x value of 0.  We will replace the x and y in the general form of the quadratic with the x and y from the table, 3 times, to find each variable. Watch how it works. We will start with (0, 15). $a(0)^2+b(0)+c=15$.  That gives us right away that c = 15.  We will do the same thing again with the second value in the table along with the fact that c = 15 to get an equation in a and b.  $a(2)^2+b(2)+15=15.5$ which simplifies to 4a+2b=.5.  Now do the same for the third set of coordinates from the table.  $a(4)^2+b(4)+15=17$ which simplifies down to 16a+4b=2.  Solve those simultaneously.  Multiply the first bolded equation by -4 and then add that one to the second bolded one.  $-4(4a+2b=.5)$ gives us -16a-8b=-2.  Add that to the second bolded equation and the a terms cancel out giving us -4b=0 so b = 0.  Subbing that back in we solve for a:  16a+4(0)=2 and 16a = 2.  Therefore, a = 1/8.  The quadratic then is $\frac{1}{8}x^2+15=y$