alechiathomas
19.07.2019 •
Mathematics
May i have with this math problem? which of the following statements are true if parabola 1 has the equation f(x)=x2+4x+3 and parabola 2 has a leading coefficient of 1 and zeros at x = -5 and x = 1. (multiple things may apply) 1. parabola 1 and parabola 2 have a zero in common. 2. parabola 1 and parabola 2 have the same line of symmetry. 3. parabola 1 crosses the y-axis higher than parabola 2. 4. parabola 1 has a lower minimum than parabola 2.
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Ответ:
f (x) = x2 + 4x + 3
f (x) = (x + 1) (x + 3)
intersection with y:
f (0) = (0) ^ 2 + 4 (0) +3
f (0) = 3
Axis of symmetry:
f '(x) = 2x + 4
2x + 4 = 0
x = -4 / 2
x = -2
Minimum of the function:
f (-2) = (- 2) ^ 2 + 4 * (- 2) +3
f (-2) = - 1
Parabola 2:
g (x) = (x + 5) (x-1)
g (x) = x ^ 2 - x + 5x - 5
g (x) = x ^ 2 + 4x - 5 intersection with y:
g (0) = (0) ^ 2 + 4 (0) - 5
g (0) = - 5
Axis of symmetry:
g '(x) = 2x + 4
2x + 4 = 0
x = -4 / 2
x = -2
Minimum of the function:
g (-2) = (- 2) ^ 2 + 4 * (- 2) - 5
g (-2) = - 9
3. Parabola 1 crosses the y-axis higher than Parabola 2.
2. Parabola 1 and Parabola 2 have the same line of symmetry.
Ответ:
c
Step-by-step explanation: