Whichgraphshowsaquadraticfunctionwhichhasadiscriminantof0?

A.

B.

7

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5

4

3

2

2

1

-7 -6 -5 -4 -3 -2

1

0

5.4

-3 -2

-1

0

N-

w

-1 -2

C.

D.

Oi

4

5

4

3

3

a

N

0

-6 -5 -4

-2

N

4

-3 -2 -1

01

2

FM

4 5

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Which graph represents a quadratic function with a discriminant of 0?

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Introduction:

Quadratic functions are an important part of mathematics and are used to solve a variety of problems. Discerning the type of quadratic function being used is essential in simplifying calculations. This article will focus on identifying the quadratic function that has a discriminant of 0, using the graphs provided.

Description:

The graphs provided depict different quadratic functions that can be employed in solving problems related to different fields. A quadratic function with a discriminant of 0 is one where the roots of the function are equal. In the graphs provided, we can see that the quadratic function is represented by a parabola that intersects the x-axis at only one point. The quadratic function is an essential part of mathematics and is used in different applications such as physics, engineering, and finance. In this article, we will analyze the different graphs and identify the one that represents a quadratic function with a discriminant of 0.

Objectives:

– To learn how to recognize quadratic functions by their graphical representation

– To understand the concept of the discriminant of a quadratic function

Learning Outcomes:

By the end of this lesson, students will be able to:

– Identify which graph depicts a quadratic function with a discriminant of 0

– Explain what the discriminant of a quadratic function represents

– Describe the shape and characteristics of a quadratic function

– Apply knowledge of quadratic functions to solve problems in real-life situations

Heading: Quadratic Functions and Discriminants.

Solution 1:

To identify which graph shows a quadratic function with a discriminant of 0, we need to look for the graph where the quadratic function touches the x-axis at only one point. This is because when the discriminant of a quadratic function is 0, the roots of the quadratic equation are equal, and therefore, the quadratic function touches the x-axis at only one point.

Upon examination of the given graphs, we see that graph C is the one which shows a quadratic function with a discriminant of 0. Therefore, the answer is C.

Solution 2:

To find out which graph represents a quadratic function with a discriminant of 0, we need to recall that the discriminant of a quadratic equation is given as b^2 – 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0. When the discriminant is equal to 0, the quadratic equation has only one root, which means the parabola intersects the x-axis at a single point.

Upon analysis of the given graphs, we can see that graph C is the graph that shows a quadratic function with a discriminant of 0. Therefore, the correct answer is C.

Suggested Resources/Books:

– “Quadratic Equations and Functions” by Marcia T. K. Chin

– “Algebra: Structure and Method, Book 1” by Richard G. Brown

– “Intermediate Algebra: Concepts and Applications” by Marvin L. Bittinger

Similar asked questions:

1. What is the significance of discriminant in a quadratic function?

2. How do you solve a quadratic equation when the discriminant is zero?

3. What is the formula for finding the discriminant of a quadratic function?

4. How do you graph a quadratic function with a given discriminant?

5. Can a quadratic function have a discriminant of zero and not have real roots?

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