SOLUTION: what can a and k be so both points are on the graph of function? points are (1,11) and (2,-19); function is y= a(x+1)^2 + k how can i find the function so that both poitns are on

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Question 105257This question is from textbook
: what can a and k be so both points are on the graph of function?
points are (1,11) and (2,-19); function is y= a(x+1)^2 + k
how can i find the function so that both poitns are on the graph?? This question is from textbook

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
One way to do these is to substitute the x- and y-values from the given points into the equation, thus giving you a system of equations with two unknowns (a and k). Then solve the system of equations for the two unknowns.
Substitute x = 1 and y = 11 from the first point (1, 11) to get the first equation.
Simplify.

Second equation:
Substitute the x- and y-values from the second point (2, -19) to get the second equation:
Simplify.

So now you have the two equatios:
1) and
2) You can solve these by any of the accepted methods for solving systems of equations. Let's use elimination by subtracting equation 1) from equation 2) and solving for a.
Divide both sides by 5.
Now substitute this value of a into either equation 1) or equation 2) and solve for k. Let's use equation 1)
Substitute a = -6

Add 24 to both sides.

Check: Into the original equation, substitute a = -6 and k = 35.

Now let's see if the two given points (1, 11) and (2, -19) satisfy this equation.

Ok for the first point.

Ok for the second point.