Quadratic Functions

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 is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

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 find the y-intercept of a quadratic function?

Back

To find the y-intercept, set x = 0 in the function and solve for f(0).

Front

What does it mean for a quadratic function to open upwards?

Back

A quadratic function opens upwards if the coefficient 'a' in the standard form f(x) = ax² + bx + c is positive.

Front

What does it mean for a quadratic function to open downwards?

Back

A quadratic function opens downwards if the coefficient 'a' in the standard form f(x) = ax² + bx + c is negative.

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 formula x = -b/(2a).

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 do you determine the number of solutions of a quadratic equation?

Back

The number of solutions can be determined using the discriminant (D = b² - 4ac): if D > 0, there are two solutions; if D = 0, there is one solution; if D < 0, there are no solutions.