Quadratic Functions Word Problems - More Practice

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 quadratic function represent?

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on the direction of the parabola.

Front

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

Back

To find the maximum height, use the formula t = -b/(2a) to find the time at which the maximum occurs, then substitute this time back into the height equation.

Front

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

Back

The 'a' value determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you determine the height of an object at a specific time using a quadratic function?

Back

Substitute the specific time value into the quadratic function to calculate the height at that time.

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 h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

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

Back

Initial height refers to the height from which an object is launched or dropped, represented as h₀ in the height equation.

Front

How can you find the time it takes for an object to reach a certain height?

Back

Set the height equation equal to the desired height and solve the resulting quadratic equation for time.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).