Quadratic Applications :-)

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 vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola (opening upwards or downwards).

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the point (0, c) where c is the constant term in the function.

Front

What is the significance of the positive zero in a quadratic function?

Back

The positive zero of a quadratic function represents the point where the function intersects the x-axis, indicating the time or position when the object reaches the ground.

Front

How can you determine the time an object is in the air using a quadratic function?

Back

To determine the time an object is in the air, find the positive zero of the quadratic function that models its height over time.

Front

What does the coefficient of the t² term indicate in a quadratic equation modeling height?

Back

The coefficient of the t² term indicates the acceleration due to gravity; a negative value shows that the object is in free fall.

Front

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

Back

The maximum height can be found by calculating the vertex of the parabola, using the formula t = -b/(2a) to find the time at which the maximum height occurs.

Front

What is the formula for the height of an object in free fall?

Back

The height of an object in free fall can be modeled by the equation h(t) = -16t² + h₀, where h₀ is the initial height.

Front

What is the initial height in the function h(t) = -16t² + 20t + 6?

Back

The initial height is 6 feet, which is the value of h when t = 0.

Front

How do you solve for the time it takes for an object to hit the ground?

Back

Set the height function h(t) equal to zero and solve for t to find the time when the object reaches the ground.