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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as y = ax² + bx + c.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a' in the equation.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph intersects the x-axis, also known as the roots or solutions of the equation.

Tags

CCSS.HSF-IF.C.7A

Front

How can you determine the number of solutions a quadratic equation has?

Back

The number of solutions can be determined using the discriminant (b² - 4ac). If it's positive, there are two solutions; if zero, one solution; if negative, no solutions.

Tags

CCSS.HSA-REI.B.4B

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 are the roots of a quadratic function?

Back

The roots are the values of x that make the quadratic equation equal to zero, also known as the solutions or x-intercepts.

Tags

CCSS.HSF-IF.C.7C

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, depending on whether it opens upwards (minimum) or downwards (maximum).

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Tags

CCSS.HSF-IF.C.7A