Quadratic Word Problems

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

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 t = -b/(2a) for the function h(t) = at² + bt + c.

Front

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

Back

To find the maximum height, determine the vertex of the parabola using t = -b/(2a) and then substitute this value back into the function to find the height.

Front

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

Back

The 'a' value determines the direction of the parabola (upward or downward) and affects the width of the parabola. A larger absolute value of 'a' makes the parabola narrower.

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 represented as the coefficient of the linear term in the height equation.

Front

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

Back

The height h(t) of an object in projectile motion can be modeled by the equation h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

How do you determine when an object will hit the ground?

Back

To determine when an object will hit the ground, set the height equation h(t) to 0 and solve for t.

Front

What is the role of gravity in projectile motion?

Back

Gravity affects the vertical motion of the projectile, causing it to accelerate downwards at a rate of approximately 32 feet per second squared.

Front

What is the maximum height of a projectile?

Back

The maximum height is the highest point reached by the projectile during its flight, found at the vertex of the parabola in its height equation.