Key Characteristics of Quadratic Functions

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 are the key characteristics of the graph of a quadratic function?

Back

The key characteristics include the vertex, axis of symmetry, x-intercepts (roots), y-intercept, and the direction of the opening (upward or downward).

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 upward or downward.

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x, typically using factoring, completing the square, or the quadratic formula.

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 equation x = -b/(2a) for the function f(x) = ax² + bx + c.

Front

What does the range of a quadratic function represent?

Back

The range represents all possible output values (y-values) of the function, which depends on the vertex and the direction the parabola opens.

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

How can you determine if a quadratic function opens upward or downward?

Back

A quadratic function opens upward if the leading coefficient (a) is positive and downward if it is negative.

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.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots (real and distinct, real and equal, or complex).