Which two points satisfy y = -x2 + 2x + 4 and x + y = 4? A. (0, 4) and (4, 0) B. (0, 4) and (3, 1) C. (7, -3) and (0, 4) D. (7,
-3) and (4, 0)
1 answer:
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Answer:
x=3
Step-by-step explanation:
Set equations equal to each other:
Subtract two from both sides
Factor out x^2 from the left side
Factor the right side, look for two factors of 9, which add to -6, which is just -3 and-3
So as you can see here, we have both sides in factored form, and both have a factor of (x-3) on both sides, and if one of the factors is zero, then the entire thing becomes zero, since 0 * anything= zero.
this means a solution would be at x=3, since it makes the right side 0 * 0 = 0, and the left side (3)^2 * 0 = 0
It's important to notice this, since had we divided by x-3 to make the equation a quadratic, we would've excluded this real solution, because when dividing by x-3 the solution x=3 makes it 0, so we would've been dividing by zero.
So one of the real solutions is at x=3
