Practice Flashcard Applications of Quadratic Functions

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 initial velocity of an object in motion modeled by a quadratic function?

Back

The initial velocity can be found by evaluating the linear coefficient (b) in the standard form of the quadratic equation s(t) = -16t² + bt + c, where b represents the initial velocity.

Front

What is the significance of the constant term in a quadratic function representing height?

Back

The constant term (c) represents the initial height of the object at time t=0.

Front

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

Back

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

Front

What is the formula to find the roots of a quadratic equation?

Back

The roots of a quadratic equation ax² + bx + c = 0 can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean when the profit function P(x) is negative?

Back

When the profit function P(x) is negative, it indicates that the business is operating at a loss.

Front

How can you determine the number of meals needed to break even in a profit function?

Back

To determine the break-even point, set the profit function P(x) equal to zero and solve for x.

Front

What is the effect of the coefficient of t² in a height equation?

Back

The coefficient of t² determines the direction of the parabola: if it is negative, the parabola opens downwards, indicating a maximum height; if positive, it opens upwards, indicating a minimum height.

Front

What is the height of an object at a specific time t in a quadratic height function?

Back

To find the height at a specific time t, substitute the value of t into the height equation h(t) and solve for h.