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.