Quadratic Word Problems

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is 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 the context of height equations, 'h' represents the height of an object above a reference point, typically the ground.

Front

What is the significance of the coefficient of t² in a quadratic height equation?

Back

The coefficient of t² determines the direction of the parabola; if it is negative, the parabola opens downward, indicating that the object reaches a maximum height.

Front

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

Back

The maximum height can be found using the formula t = -b/(2a), where a and b are the coefficients from the quadratic equation h = at² + bt + c.

Front

What does the vertex of a parabola represent in a height equation?

Back

The vertex of a parabola represents the maximum or minimum height of the object, depending on the direction the parabola opens.

Front

In the equation h = -16t² + vt + s, what do v and s represent?

Back

In the equation, v represents the initial upward velocity, and s represents the initial height from which the object is launched.

Front

How can 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 = 0 and solve for t.

Front

What is the formula to calculate the time of flight for a projectile?

Back

The time of flight can be calculated using the formula t = (2v)/g, where v is the initial velocity and g is the acceleration due to gravity.

Front

What is the role of gravity in quadratic height equations?

Back

Gravity is represented by the negative coefficient of t² in the height equation, indicating that it pulls the object downward.

Front

How do you interpret the initial height in a height equation?

Back

The initial height is the value of h when t = 0, representing the starting position of the object before it begins to move.