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 (opening upwards or downwards).

Front

How can you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function can be found at the vertex, which occurs at x = -b/(2a) for the function f(x) = ax² + bx + c.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of a quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How do you find the height of an object modeled by a quadratic function at a specific time?

Back

To find the height of an object at a specific time, substitute the time value into the quadratic function that models the height.

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, where a, b, and c are constants.

Front

What does the term 'parabola' refer to in the context of quadratic functions?

Back

A parabola is the graph of a quadratic function, which is a U-shaped curve that can open upwards or downwards.

Front

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

Back

To determine when an object will hit the ground, set the height function equal to zero and solve for the time variable.

Front

What is the formula for the height of an object in projectile motion?

Back

The height of an object in projectile motion can be modeled by the equation h(t) = -gt² + v₀t + h₀, where g is the acceleration due to gravity, v₀ is the initial velocity, and h₀ is the initial height.

Front

What does the coefficient of the x² term indicate about the direction of a parabola?

Back

If the coefficient of the x² term (a) is positive, the parabola opens upwards; if it is negative, the parabola opens downwards.