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 graph of a quadratic equation look like?

Back

The graph of a quadratic equation is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

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

Front

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

Back

The maximum height can be found by calculating the vertex of the parabola, using the formula h = -b²/(4a) + c, where h is the maximum height.

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.

Front

What does the 't' represent in the height equations?

Back

In the height equations, 't' represents the time in seconds after the object was thrown or launched.

Front

How do you determine when an object returns to the ground using a quadratic equation?

Back

To find when an object returns to the ground, set the height equation h(t) = 0 and solve for 't'.

Front

What is the formula for the height of an object thrown upwards?

Back

The height of an object thrown upwards can be modeled by the equation h(t) = -at² + bt + c, where 'a' is the acceleration due to gravity, 'b' is the initial velocity, and 'c' is the initial height.

Front

What is the role of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

How do you find the time at which a projectile reaches its maximum height?

Back

The time at which a projectile reaches its maximum height can be found using the formula t = -b/(2a) from the quadratic equation.