Question

May I please have help 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.

Answer 1

Parabola 1:
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

Answer:
3. Parabola 1 crosses the y-axis higher than Parabola 2.
2. Parabola 1 and Parabola 2 have the same line of symmetry.