Answer:
y = 4x² -3x +5
Step-by-step explanation:
Often the easiest strategy is to check the answers. (We will refer to them as choices A–D.)
The three data points show a minimum value in the middle, so the graph opens upward. This eliminates choices A and B that both have graphs that open downward.
All the answer equations agree with the table for x = 0. (Their constants are all +5.) Choices C and D also agree with the table for x = -1. (Put -1 where x is in the equation and do the arithmetic.)
Only choice D agrees with the table for x = 2. (Again, put 2 where x is and evauate the function.)
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Equation D evaluated for x=2:
... f(2) = 4·2² -3·2 +5 = 16 -6 +5 = 15 . . . . matches the table
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If you want to actually find the equation without reference to the answer choices, you can fill in the table values to write 3 equations in 3 unknowns:
y = ax² +bx +c
12 = a(-1)² +b(-1) +c ⇒ a -b +c = 12
5 = a·0² +b·0 +c ⇒ c = 5
15 = a·2² +b·2 +c ⇒ 4a +2b +c = 15
Substituting the value of c found in the second equation into the first two equations, they become ...
- a -b = 7
- 4a +2b = 10 ⇒ 2a +b = 5 . . . . after dividing by 2
We can add these two equations to eliminate the b variable and get
... 3a = 12 ⇒ a = 4
Putting this into the first equation, we get
... 4 - b = 7
... -3 = b . . . . . . add b-7
Now, we have all three coefficients, so we know the function is ...
... f(x) = 4x² -3x +5
