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).

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSA-REI.B.4B

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).

Tags

CCSS.HSA-REI.B.4B