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

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

Three properties that are universal to all quadratic functions: 1) The graph of a quadratic function is always a parabola that either opens upward or downward (end behavior); 2) The domain of a quadratic function is all real numbers; and 3) The vertex is the lowest point when the parabola opens upwards; while the …

What are the characteristics of a quadratic equation?

• A parabola that opens upward contains a vertex that is a minimum point.
• Standard form is y = ax2 + bx + c, where a≠ 0.
• The graph is a parabola.
• The x-intercepts are the points at which a parabola intersects the x-axis.

What are the concepts of quadratic functions?

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in “width” or “steepness”, but they all have the same basic “U” shape.

What is the discriminant of a quadratic graph?

The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.

What are the 5 key features of a quadratic graph?

There are many key features in a quadratic graph such as the zeroes (x-intercepts, also known as the roots), y-intercept, axis of symmetry, and the vertex.

How do you describe a quadratic graph?

The graph of a quadratic function is a U-shaped curve called a parabola. The extreme point ( maximum or minimum ) of a parabola is called the vertex, and the axis of symmetry is a vertical line that passes through the vertex. The x-intercepts are the points at which the parabola crosses the x-axis.

What are the 5 key features for graphing the quadratic function?

Summary

• Vertex: The point where the function changes direction.
• Axis of Symmetry: The vertical line that splits the parabola in half.
• Maximum/Minimum Value: Graphs that open upwards have a minimum, and graphs that open downwards have a maximum.
• y-intercept: The point where the parabola crosses the y-axis.

What are examples of quadratic functions?

Examples of quadratic equations in other forms include:

• x(x – 2) = 4 [upon multiplying and moving the 4, becomes x² – 2x – 4 = 0]
• x(2x + 3) = 12 [upon multiplying and moving the 12, becomes 2x² – 3x – 12 = 0]
• 3x(x + 8) = -2 [upon multiplying and moving the -2, becomes 3x² + 24x + 2 = 0]

What is the concept of lines and quadratic functions?

Key Concepts A polynomial function of degree two is called a quadratic function. The graph of a quadratic function is a parabola. A parabola is a U-shaped curve that can open either up or down. The axis of symmetry is the vertical line passing through the vertex. The domain of a quadratic function is all real numbers.

What is the vertex form of a quadratic function?

The vertex form of a quadratic function is f(x) = a(x – h)2 + k, where a, h, and k are constants.

How do you know if a discriminant is zero?

If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots. Therefore, there are two real, identical roots to the quadratic equation x2 + 2x + 1. D > 0 means two real, distinct roots.

How do you tell if a graph has a positive discriminant?

Anytime the discriminant is positive, the graph will cross the x-axis twice. The discriminant won’t tell you the actual answers. It doesn’t tell you exactly where the graph crosses the x-axis, but it can tell you how many solutions and how many times it crosses.

How is the graph of a quadratic function transformed?

The standard form is useful for determining how the graph is transformed from the graph of y= x2 y = x 2. The figure below is the graph of this basic function. You can represent a vertical (up, down) shift of the graph of f (x) =x2 f ( x) = x 2 by adding or subtracting a constant, k k.

What makes a graph traversable in graph theory?

A graph is traversable if you can draw a path between all the vertices without retracing the same path. Based on this path, there are some categories like Euler’s path and Euler’s circuit which are described in this chapter. An Euler’s path contains each edge of ‘G’ exactly once and each vertex of ‘G’ at least once.

What are the key terms of a quadratic graph?

Key Terms 1 vertex: The point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function. 2 axis of symmetry: A vertical line drawn through the vertex of a parabola around which the parabola is symmetric. 3 zeros: In a given function, the values of x x at which y= 0 y = 0, also called roots.

How to calculate the vertical shift of a quadratic function?

You can represent a vertical (up, down) shift of the graph of f (x) =x2 f ( x) = x 2 by adding or subtracting a constant, k k. If k > 0 k > 0, the graph shifts upward, whereas if k < 0 k < 0, the graph shifts downward. Determine the equation for the graph of f (x) =x2 f ( x) = x 2 that has been shifted up 4 units.