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 height equations?

Back

In height equations, 'h' represents the height of an object at a given time 't'.

Front

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

Back

The coefficient of t² determines the direction of the parabola: if it is negative, the parabola opens downwards, indicating a maximum point; if positive, it opens upwards, indicating a minimum point.

Front

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

Back

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

Front

What is the vertex of a parabola in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation, and can be found using the formula t = -b/(2a) for the equation ax² + bx + c.

Front

How do you determine the maximum height of a projectile?

Back

The maximum height can be found by calculating the vertex of the quadratic equation that models the height.

Front

What does the term 'maximum profit' mean in a profit function?

Back

Maximum profit refers to the highest possible profit that can be achieved, which occurs at the vertex of the profit function's quadratic equation.

Front

How can you model the height of an object thrown into the air?

Back

The height can be modeled using a quadratic equation of the form h(t) = -at² + bt + c, where a, b, and c are constants.

Front

What is the formula to find the time at which a projectile reaches its maximum height?

Back

The time at which a projectile reaches its maximum height is given by t = -b/(2a) from the quadratic equation ax² + bx + c.

Front

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

Back

Initial height refers to the height from which the object is launched, represented by the constant term in the height equation.