Key Characteristics of Quadratic Functions

Front

What are the zeros of a quadratic function?

Back

The zeros (or roots) of a quadratic function are the values of x for which the function equals zero. They can be found by factoring, using the quadratic formula, or graphing.

Front

What is the vertex of a quadratic function?

Back

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

Front

How do you determine if a quadratic function has a maximum or minimum vertex?

Back

If the coefficient of the x^2 term is negative, the vertex is a maximum. If it is positive, the vertex is a minimum.

Front

What does it mean for a quadratic graph to open upwards or downwards?

Back

A quadratic graph opens upwards if the coefficient of x^2 is positive, and it opens downwards if the coefficient is negative.

Front

What is the y-intercept of a quadratic function?

Back

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

Front

What is the range of a quadratic function that opens upwards?

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex.

Front

How can you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)) where f(x) is the quadratic function.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the factored form of a quadratic function?

Back

The factored form is f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots of the function.