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 represents the maximum or minimum value of the quadratic function.

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) to find the time at which the maximum height occurs, then substituting this time back into the height equation.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

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

Front

What is the formula to find the height of an object in projectile motion?

Back

The height h at time t can be modeled by the equation h = -at² + bt + c, where a, b, and c are constants.

Front

How do you determine the time it takes for an object to reach its maximum height?

Back

The time to reach maximum height is found using the formula t = -b/(2a) from the quadratic equation h = -at² + bt + c.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

How do you calculate the height of a projectile at a specific time?

Back

Substitute the specific time value into the height equation h = -at² + bt + c to find the height at that time.

Front

What does the 'c' value represent in a quadratic equation?

Back

The 'c' value represents the y-intercept of the parabola, which is the height of the object at time t = 0.