# Characteristics of quadratic functions equations

## What are the 4 key features of a quadratic function?

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**.## What are the characteristics of the graph of a quadratic equation?

The graph of a quadratic function is a U-shaped curve called a parabola. One important feature of the graph is that

**it has an extreme point, called the vertex**. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function.## What are the characteristics of the roots of a quadratic equation?

The roots of a quadratic equation with real coefficients are

**real and distinct**if $D={{b}^{2}}-4ac>0$. Roots are a conjugate pair of complex roots if $D={{b}^{2}}-4ac<0$. The roots will be rational when $D={{b}^{2}}-4ac$ is a perfect square. If the discriminant is not a perfect square, then the roots are irrational.## How do you identify a function of a quadratic equation?

A quadratic function is one of the form

**f(x) = ax**. 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.^{2}+ bx + c, where a, b, and c are numbers with a not equal to zero## What represents a quadratic function?

Quadratic functions can be represented symbolically by the equation,

**y(x) = ax**, where a, b, and c are constants, and a â‰ 0. This form is referred to as standard form.^{2}+ bx + c## Which of the following is a quadratic equation example?

Examples of the standard form of a quadratic equation (axÂ² + bx + c = 0) include:

**6xÂ² + 11x – 35 = 0**. 2xÂ² – 4x – 2 = 0. -4xÂ² – 7x +12 = 0.## What are the 3 types of quadratic equations?

**There are three commonly-used forms of quadratics:**

- Standard Form: y = a x 2 + b x + c y=ax^2+bx+c y=ax2+bx+c.
- Factored Form: y = a ( x âˆ’ r 1 ) ( x âˆ’ r 2 ) y=a(x-r_1)(x-r_2) y=a(xâˆ’r1)(xâˆ’r2)
- Vertex Form: y = a ( x âˆ’ h ) 2 + k y=a(x-h)^2+k y=a(xâˆ’h)2+k.

## What are the parts of a quadratic equation?

MathHelp.com. The Quadratic Formula uses the

**“a”, “b”, and “c”**from “ax^{2}+ bx + c”, where “a”, “b”, and “c” are just numbers; they are the “numerical coefficients” of the quadratic equation they’ve given you to solve.## What is an example of a quadratic function?

Quadratic Function Examples

The quadratic function equation is f(x) = ax^{2} + bx + c, where a â‰ 0. Let us see a few examples of quadratic functions: **f(x) = 2x ^{2} + 4x – 5**; Here a = 2, b = 4, c = -5. f(x) = 3x

^{2}– 9; Here a = 3, b = 0, c = -9.

## What is the graph of a quadratic equation?

The graph of a quadratic function is called

**a parabola**and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.## Which description of a graph appears to represent a quadratic relation?

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.## What are the characteristics of a linear function?

Linear functions are those whose graph is a straight line. A linear function has

**one independent variable and one dependent variable**. The independent variable is x and the dependent variable is y. a is the constant term or the y intercept.## What are the characteristics of a polynomial function?

A polynomial function consists of either zero or the sum of a finite number of non-zero terms, each of which is a product of a number, called the coefficient of the term, and a variable raised to a non-negative integer power.

## What is the general form of quadratic equation?

Hence,the general form of quadratic equation is

**a x 2 + b x + c = 0**.**Q**.## What is the range of quadratic function?

If a quadratic function opens up, then the range is

**all real numbers greater than or equal to the y-coordinate of the range**. If a quadratic function opens down, then the range is all real numbers less than or equal to the y-coordinate of the range.## What is a real life example of a quadratic function?

**Throwing a ball, shooting a cannon, diving from a platform and hitting a golf ball**are all examples of situations that can be modeled by quadratic functions. In many of these situations you will want to know the highest or lowest point of the parabola, which is known as the vertex.

## How many types of quadratic equations are there?

three different forms

There are

**three**different forms of quadratic equations, and they are: Standard form: The standard form of a quadratic equation is represented by y = a x 2 + b x + c where and are just the numbers.