Quadratic Word Problems

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 (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 that 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 (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

How can you determine the time it takes for an object to hit the ground using a quadratic function?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as ax² + bx + c = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you interpret the height function h(t) = -16t² + vt + h0?

Back

In this function, -16t² represents the effect of gravity, v is the initial velocity, and h0 is the initial height from which the object is launched.

Front

What is the role of initial velocity in projectile motion?

Back

Initial velocity determines how high and how far the object will travel before it starts to fall back down.