Quadratic Word Problems

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the variable 'h' represent in the context of height equations?

Back

In height equations, 'h' represents the height of an object above a reference point, often measured in feet or meters.

Front

What does the variable 't' represent in the context of motion equations?

Back

In motion equations, 't' represents time, usually measured in seconds.

Front

How do you find the maximum height of a quadratic function?

Back

The maximum height of a quadratic function in the form h(t) = at² + bt + c can be found using the formula t = -b/(2a) to find the time at which the maximum occurs.

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

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you determine when an object reaches the ground using a height equation?

Back

To determine when an object reaches the ground, set the height equation h(t) = 0 and solve for t.

Front

What is the formula for the height of an object in free fall?

Back

The height of an object in free fall can be modeled by the equation h(t) = -16t² + h₀, where h₀ is the initial height.

Front

What does the term 'initial velocity' refer to in motion problems?

Back

Initial velocity refers to the speed and direction of an object at the moment it begins its motion.

Front

How can you find the time it takes for an object to reach maximum height?

Back

To find the time it takes for an object to reach maximum height, use the formula t = -b/(2a) from the quadratic equation.