Projectile Motion (Quadratics)

Front

What is projectile motion?

Back

Projectile motion is the motion of an object thrown into the air, subject to the force of gravity, following a curved path called a trajectory.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent in projectile motion?

Back

The vertex represents the maximum height of the projectile when it is thrown upwards.

Front

How do you find the maximum height of a projectile?

Back

The maximum height can be found using the formula h = -b²/(4a) + c, where the quadratic is in the form ax² + bx + c.

Front

What is the effect of gravity on projectile motion?

Back

Gravity accelerates the projectile downwards, affecting its vertical motion and causing it to follow a parabolic path.

Front

What is the formula for the height of a projectile at time t?

Back

The height h at time t is given by h = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

What is the significance of the x-intercepts in a quadratic function?

Back

The x-intercepts represent the points where the projectile hits the ground (height = 0).

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the value b² - 4ac, which determines the nature of the roots (real and distinct, real and equal, or complex).