Answer: (-1, 6)
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Explanation:
f(x) is equal to both x^2-2x+3 and also -6x at the same time. Set those two expressions equal to one another and solve for x.
x^2-2x+3 = -6x
x^2-2x+3+6x = 0
x^2+4x+3 = 0
(x+3)(x+1) = 0 .... see note below
x+3 = 0 or x+1 = 0
x = -3 or x = -1
Note: 3 and 1 multiply to 3, and also add to 4.
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Once we get the x values, we plug them into either equation to find the y value.
So if x = -3, then
f(x) = x^2-2x+3
f(-3) = (-3)^2-2(-3)+3
f(-3) = 9 + 6 + 3
f(-3) = 18
or we could say
f(x) = -6x
f(-3) = -6(-3)
f(-3) = 18
Both versions produce the same output when x = -3.
The second version is easier to work with.
Since x = -3 leads to y = 18, we know that (-3, 18) is one of the solutions. That explains where your teacher got (-3, 18) from.
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We'll use this idea for x = -1 now
f(x) = x^2-2x+3
f(-1) = (-1)^2-2(-1)+3
f(-1) = 1 + 2 + 3
f(-1) = 6
or we could say
f(x) = -6x
f(-1) = -6(-1)
f(-1) = 6
Like before, both versions of f(x) produce the same output when the input is x = -1.
The other solution is (-1, 6)
