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 vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola (opening upwards or downwards).

Front

How do you find the maximum height of a projectile modeled by a quadratic equation?

Back

To find the maximum height, use the formula t = -b/(2a) to find the time at which the maximum height occurs, then substitute this value back into the height equation.

Front

What is the significance of the 'h' in the height equations?

Back

In the context of projectile motion, 'h' represents the height of the object above the ground at any given time 't'.

Front

What does the coefficient of t² indicate in a height equation?

Back

The coefficient of t² indicates the acceleration due to gravity in feet per second squared, typically -16 in feet for objects in free fall.

Front

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

Back

Set the height equation h(t) = 0 and solve for t to find the time when the object reaches the ground.

Front

What is the formula to calculate the height of a projectile at a given time?

Back

The height of a projectile can be calculated using the formula h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

What does the initial velocity represent in a height equation?

Back

The initial velocity represents the speed at which the object is launched or thrown at time t = 0.

Front

How can you find the height of an object at a specific time using a quadratic equation?

Back

Substitute the specific time value into the height equation h(t) to calculate the height at that time.

Front

What is the role of the constant term in a quadratic height equation?

Back

The constant term represents the initial height from which the object is launched or the height of the starting point.