Quadratic Real World Problems #2

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + 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 (upward or downward).

Front

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

Back

The maximum height can be found using the formula t = -b/(2a) to determine the time at which the maximum height occurs, then substituting this time back into the height function.

Front

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

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, the parabola opens upward; if a < 0, it opens downward.

Front

How can you determine when a projectile will hit the ground using a quadratic function?

Back

Set the height function equal to zero and solve for t. The positive value of t will indicate when the projectile hits the ground.

Front

What does the y-intercept of a quadratic function represent in a real-world context?

Back

The y-intercept represents the initial height of the object at time t = 0.

Front

How do you interpret the roots of a quadratic equation in a real-world problem?

Back

The roots of a quadratic equation represent the times at which the projectile is at a height of zero (e.g., when it hits the ground).

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) = -16t^2 + v_0t + h_0, where v_0 is the initial velocity and h_0 is the initial height.

Front

What is the initial height of a projectile if the height function is h(t) = -5t^2 + 40t + 2?

Back

The initial height is given by the constant term, which is 2 meters.

Front

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

Back

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