Key Properties of Quadratics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What shape does the graph of a quadratic function take?

Back

The graph of a quadratic function is called a parabola.

Front

What are the two types of parabolas based on their orientation?

Back

Parabolas can open upwards (minimum value) or downwards (maximum value).

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the quadratic equation in standard form.

Front

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

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

If the coefficient 'a' is positive, the parabola opens upwards and has a minimum value. If 'a' is negative, it opens downwards and has a maximum value.

Front

What is the formula to find the vertex of a quadratic function given in standard form?

Back

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