+64 Passes through (-5, 0), (1,0), and (-3, -16)
Is even and has a range of y < 2
Passes through (0, 0), (2, 2), and (4, 0)
+33661 A general quadratic function can be written as y = a*x^2 + b*x + c, where a, b and c are constants to be found.
For "Passes through (-5, 0), (1,0), and (-3, -16)" :
(-5,0) 0 = 25a - 5b + c
(1,0) 0 = a + b + c
(-3,-16) -16 = 9a - 3b + c
You now have 3 equations in the 3 unknowns so you should be able to solve for a, b and c (you should get a=2, b=8 and c=-10)
For "Is even and has a range of y<= 2":
Note that y(-x) = y(x) which means b = 0.
The maximum value of y is obtained when 2*a*x + b = 0 or x = 0 (can't have a = 0 or it wouldn't be quadratic).
So must have c = 2. y = a*x^2 + 2. For y to have a maximum value of 2, a must be negative.
For "Passes through (0, 0), (2, 2), and (4, 0)" use the same method as the first above.
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