Projectile Motion and Quadratics

Front

What are the X-Intercepts, Roots, Zeros, and Solutions of a quadratic equation?

Back

The X-Intercepts, Roots, Zeros, and Solutions of a quadratic equation are the values of x where the graph intersects the x-axis. For the equation given, they are {-8, 0}.

Front

How do you determine the maximum height of a projectile from a graph?

Back

The maximum height of a projectile can be determined from the graph by identifying the vertex of the parabola, which represents the highest point. In the case of the rocket, it took 7 seconds to reach its maximum height.

Front

What is the height of an object at time t = 0 in the function h(t) = -16t^2 + 80t + 200?

Back

The height of the object at t = 0 is 200 feet.

Front

What does the term 'initial height' refer to in projectile motion?

Back

The initial height refers to the height of the object at the start of its motion, which is the value of h when t = 0. In the equation h = -16t^2 + 64t + 960, the initial height is 960 feet.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants.

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

How can you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form can be found using the formula x = -b/(2a), where a and b are the coefficients from the equation ax^2 + bx + c.

Front

What is the formula for the height of a projectile in motion?

Back

The formula for the height of a projectile in motion is h(t) = -16t^2 + vt + h0, where v is the initial velocity and h0 is the initial height.

Front

What does the term 'parabola' refer to in the context of projectile motion?

Back

A parabola is the U-shaped graph that represents the trajectory of a projectile under the influence of gravity.

Front

How do you calculate the time of flight for a projectile?

Back

The time of flight can be calculated by finding the total time it takes for the projectile to reach the ground, which can be determined by solving the quadratic equation for when h(t) = 0.