day 1 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 projectile motion?

Back

In projectile motion, 'h' represents the height of the object above a reference point, often the ground, at a given time 't'.

Front

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

Back

The coefficient of t² determines the direction of the parabola: if it is negative, the parabola opens downward, indicating that the object will reach a maximum height and then fall.

Front

How do you find the time when an object returns to the ground in a quadratic height equation?

Back

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

Front

What is the formula to find the maximum height of a projectile?

Back

The maximum height can be found using the vertex formula: h = -b²/(4a) + c, where a, b, and c are from the quadratic equation h = at² + bt + c.

Front

What does the term 'initial velocity' mean in projectile motion?

Back

Initial velocity is the speed at which an object is launched or thrown at the beginning of its motion, often measured in feet per second (ft/s).

Front

How do you determine the time to reach maximum height in a quadratic equation?

Back

The time to reach maximum height can be found using the formula t = -b/(2a), where a and b are coefficients from the height equation.

Front

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

Back

The constant term represents the initial height of the object at time t = 0, indicating how high above the ground the object starts.

Front

What is the effect of changing the coefficient of t in a height equation?

Back

Changing the coefficient of t affects the initial velocity of the object; a higher coefficient results in a greater initial upward speed.

Front

How can you interpret the graph of a quadratic height equation?

Back

The graph of a quadratic height equation is a parabola that shows the height of the object over time, with the vertex representing the maximum height.