LT #8 Modeling

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of a parabola, depending on its orientation. It represents the maximum or minimum value of the quadratic function.

Front

How do you find the x-coordinate of the vertex in a quadratic equation?

Back

Use the formula x = -b/(2a), where a and b are coefficients from the quadratic equation in the form y = ax^2 + bx + c.

Front

What does the y-intercept represent in a graph?

Back

The y-intercept is the point where the graph intersects the y-axis, indicating the value of y when x = 0.

Front

What is the significance of the x-intercept in a real-world context?

Back

The x-intercept represents the point where a function's output (y) is zero, often indicating a critical point such as when an object hits the ground.

Front

How can you determine the maximum height of a projectile using its equation?

Back

To find the maximum height, use the x-coordinate of the vertex (x = -b/(2a)) to find the corresponding y-value in the equation.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax^2 + bx + c.

Front

What does the term 'projectile motion' refer to?

Back

Projectile motion describes the motion of an object that is thrown or projected into the air, subject to the force of gravity.

Front

What is the formula for the height of a projectile at time t?

Back

The height h(t) can be modeled by the equation h(t) = -16t^2 + vt + h0, where v is the initial velocity and h0 is the initial height.

Front

What does the term 'maximum height' mean in the context of projectile motion?

Back

Maximum height is the highest vertical position reached by a projectile during its flight.

Front

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

Back

Use the formula t = -b/(2a) from the height equation h(t) = at^2 + bt + c.