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kholman
30.05.2020 •
Mathematics
Which line(s) intersect the parabola y = x^2 − 3x + 4 at two points? Select all that apply. A. y = –3x + 2 B. y = –3x + 3 C. y = –3x + 5 D. y = –3x + 6
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Ответ:
C and D
Step-by-step explanation:
Equating the line A and the parabola, we get
-3x + 2 = x² - 3x + 4
0 = x² - 3x + 4 +3x - 2
0 = x² + 2
-2 = x²
which has no real solutions. Then, the line A and the parabola don't intersect each other.
Equating the line B and the parabola, we get
-3x + 3 = x² - 3x + 4
0 = x² - 3x + 4 + 3x - 3
0 = x² + 1
-1 = x²
which has no real solutions. Then, the line B and the parabola don't intersect each other.
Equating the line C and the parabola, we get
-3x + 5 = x² - 3x + 4
0 = x² - 3x + 4 + 3x - 5
0 = x² - 1
1 = x²
√1 = x
which has 2 solutions, x = 1 and x = -1. Then, the line C and the parabola intersect each other.
Equating the line D and the parabola, we get
-3x + 6 = x² - 3x + 4
0 = x² - 3x + 4 + 3x - 6
0 = x² - 2
2 = x²
√2 = x
which has 2 solutions, x ≈ 1.41 and x ≈ -1.41. Then, the line D and the parabola intersect each other.
Ответ:
im pretty sure the answer is A
Step-by-step explanation: