Key Features of 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 vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on the direction of the parabola.

Front

What does the axis of symmetry represent in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, and it passes through the vertex.

Front

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

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

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 are the zeros (or roots) of a quadratic function?

Back

The zeros are the x-values where the graph intersects the x-axis, found by solving the equation f(x) = 0.

Front

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

Back

The range is the set of all y-values that the function can take, starting from the y-coordinate of the vertex to positive infinity.

Front

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

Back

The range is the set of all y-values that the function can take, starting from the y-coordinate of the vertex to negative infinity.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

If the leading coefficient (a) is positive, the parabola opens upwards; if it is negative, the parabola opens downwards.

Front

What is the standard form of a quadratic function?

Back

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