1) Choose True or False.

Question

If the coefficient in front of the x^2 in a quadratic equation is negative, the parabola will curve up.

If the parabola intersects the x-axis at two points, the axis of symmetry will be halfway between the two points of intersection.

Factoring should always be used to solve quadratic equations.

Answer 1

Let's evaluate each statement one by one:

1. If the coefficient in front of the \( x^2 \) in a quadratic equation is negative, the parabola will curve up.

   • False. If the coefficient in front of \( x^2 \) is negative, the parabola opens downward.

2. If the parabola intersects the x-axis at two points, the axis of symmetry will be halfway between the two points of intersection.

   • True. The axis of symmetry for a parabola that intersects the x-axis at two points is indeed located at the midpoint of those two points.

3. Factoring should always be used to solve quadratic equations.

   • False. While factoring is one method to solve quadratic equations, it is not always applicable or the best choice. Other methods include completing the square and using the quadratic formula, which can be used in situations where factoring is difficult or not possible.

So the answers are:

1. False
2. True
3. False