Applications of Quadratics Exit Ticket

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically 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 x-value of the vertex in a quadratic function?

Back

The x-value of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients from the quadratic equation in standard form.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, which occurs when x = 0. It is represented by the value of c in the quadratic equation.

Front

What does the positive zero of a quadratic function indicate?

Back

The positive zero of a quadratic function indicates the x-value(s) where the function's output is zero, meaning the points where the graph intersects the x-axis.

Front

How can you determine the maximum height of an object thrown in the air using a quadratic function?

Back

The maximum height can be found by calculating the y-value of the vertex of the quadratic function that models the object's height over time.

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 + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

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

Back

The initial height refers to the height from which an object is thrown or dropped, represented by h₀ in the height equation.

Front

How do you interpret the coefficients in a quadratic function?

Back

In the quadratic function f(x) = ax² + bx + c, 'a' determines the direction and width of the parabola, 'b' affects the position of the vertex, and 'c' represents the y-intercept.

Front

What is the relationship between the roots of a quadratic function and its graph?

Back

The roots (or zeros) of a quadratic function are the x-values where the graph intersects the x-axis, indicating the solutions to the equation f(x) = 0.