Quadratic Applications :-)

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 quadratic function represent?

Back

The vertex of a quadratic function represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, which occurs when x = 0. It represents the initial value of the function.

Front

How do you find the time it takes for an object to hit the ground in a quadratic model?

Back

To find the time it takes for an object to hit the ground, set the height function h(t) equal to zero and solve for t.

Front

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

Back

The term 'positive zero' refers to the positive solution of the equation when finding the x-intercepts of the quadratic function, indicating 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 formula to find the vertex of a quadratic function?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h).

Front

What does the coefficient 'a' in a quadratic function indicate about the graph?

Back

The coefficient 'a' indicates the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens 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 occurs at the vertex, which can be found using the vertex formula.

Front

What is the quadratic formula?

Back

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