Quadratic Function Word Problems - FLASHCARD

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

The maximum height can be found using the 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 significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the standard form of a quadratic function?

Back

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

Front

How do you determine when a projectile hits the ground using a quadratic function?

Back

To determine when a projectile hits the ground, set the height function h(t) equal to 0 and solve for t.

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) = -4.9t² + v₀t + h₀, where v₀ is the initial velocity and h₀ is the initial height.

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 round to the nearest tenth?

Back

To round to the nearest tenth, look at the hundredths place: if it's 5 or more, round up; if it's less than 5, round down.

Front

What is the formula to find the height of a projectile at a given time?

Back

The height of a projectile at time t is given by h(t) = -gt² + v₀t + h₀, where g is the acceleration due to gravity.