Subjects

Subjects

More

Search

AI Knowunity

Subjects

/

Pre-Calculus

/

Ellipses & hyperbola

/

Introduction to hyperbolas

What's a Quadratic Function? Find Parabola Vertex & Baseball Height!

View

What's a Quadratic Function? Find Parabola Vertex & Baseball Height!
user profile picture

Chelsea

@zuncho

·

625 Followers

Follow

A comprehensive guide to quadratic functions and their practical applications in mathematics and real-world scenarios.

• The definition of a quadratic function in math is expressed as f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.
• Understanding parabolas and their properties is crucial, including their orientation (upward or downward) based on the leading coefficient.
• Key concepts include vertex form, axis of symmetry, and how to find the vertex of a parabola using different methods.
• Real-world applications are explored, including maximum height calculation of a baseball using quadratic function.
• Advanced topics cover writing equations of parabolas and analyzing data using quadratic regression.

4/5/2023

143

Section 2.1 Quadratic Functions Definition of a Quadratic Function ● ● ● Let a, b, and c be real numbers with a # 0, The function f(x)= a ●

View

Page 3: Real-World Applications

This page demonstrates practical applications of quadratic functions, focusing on projectile motion and baseball trajectory analysis.

Example: A baseball problem shows how to calculate maximum height using the function f(x) = -0.0032x² + x + 3.

Highlight: The completing the square method provides an alternative approach to finding the vertex.

Vocabulary: Maximum height in projectile motion occurs at the vertex of the parabola.

Section 2.1 Quadratic Functions Definition of a Quadratic Function ● ● ● Let a, b, and c be real numbers with a # 0, The function f(x)= a ●

View

Page 5: Data Analysis and Regression

This page explores the practical application of quadratic functions in data analysis, specifically focusing on automobile speed and mileage relationships.

Example: A scatter plot of speed versus mileage data is analyzed using quadratic regression.

Highlight: The quadratic regression model y = -0.008199800x² + 0.746113886x + 13.46863137 best fits the data.

Vocabulary: Quadratic regression is used to find the best-fitting parabola for a set of data points.

Section 2.1 Quadratic Functions Definition of a Quadratic Function ● ● ● Let a, b, and c be real numbers with a # 0, The function f(x)= a ●

View

Page 4: Writing Parabola Equations

This page focuses on constructing quadratic equations given specific conditions, particularly using vertex form.

Definition: The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h,k) is the vertex.

Example: Writing an equation for a parabola with vertex (1,2) passing through (0,0) yields f(x) = -2(x-1)² + 2.

Highlight: The process involves using given points to determine the value of 'a' in vertex form.

Section 2.1 Quadratic Functions Definition of a Quadratic Function ● ● ● Let a, b, and c be real numbers with a # 0, The function f(x)= a ●

View

Page 1: Introduction to Quadratic Functions

This page introduces the fundamental concepts of quadratic functions and their graphical representations. The standard form and vertex form of quadratic functions are thoroughly explained, along with their key characteristics.

Definition: A quadratic function in standard form is f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.

Highlight: The leading coefficient 'a' determines whether the parabola opens upward (positive a) or downward (negative a).

Vocabulary: The axis of symmetry is a vertical line that divides the parabola into two identical halves.

Example: For f(x) = -2(x - 3)² + 6, the vertex is at (3,6) and the axis of symmetry is x = 3.

Section 2.1 Quadratic Functions Definition of a Quadratic Function ● ● ● Let a, b, and c be real numbers with a # 0, The function f(x)= a ●

View

Page 2: Finding the Vertex

This page details various methods for finding the vertex of a quadratic function, particularly focusing on functions in standard form and their graphical representations.

Definition: The vertex formula for a quadratic function in standard form is h = -b/(2a), where (h,k) represents the vertex coordinates.

Example: For g(x) = x² + 2x + 1, the vertex is calculated as (-1,0) using the vertex formula.

Highlight: The x-intercepts can be found using the quadratic formula when the function equals zero.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Subjects

/

Pre-Calculus

/

Ellipses & hyperbola

/

Introduction to hyperbolas

What's a Quadratic Function? Find Parabola Vertex & Baseball Height!

user profile picture

Chelsea

@zuncho

·

625 Followers

Follow

A comprehensive guide to quadratic functions and their practical applications in mathematics and real-world scenarios.

• The definition of a quadratic function in math is expressed as f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.
• Understanding parabolas and their properties is crucial, including their orientation (upward or downward) based on the leading coefficient.
• Key concepts include vertex form, axis of symmetry, and how to find the vertex of a parabola using different methods.
• Real-world applications are explored, including maximum height calculation of a baseball using quadratic function.
• Advanced topics cover writing equations of parabolas and analyzing data using quadratic regression.

4/5/2023

143

 

Pre-Calculus

4

Section 2.1 Quadratic Functions Definition of a Quadratic Function ● ● ● Let a, b, and c be real numbers with a # 0, The function f(x)= a ●

Page 3: Real-World Applications

This page demonstrates practical applications of quadratic functions, focusing on projectile motion and baseball trajectory analysis.

Example: A baseball problem shows how to calculate maximum height using the function f(x) = -0.0032x² + x + 3.

Highlight: The completing the square method provides an alternative approach to finding the vertex.

Vocabulary: Maximum height in projectile motion occurs at the vertex of the parabola.

Section 2.1 Quadratic Functions Definition of a Quadratic Function ● ● ● Let a, b, and c be real numbers with a # 0, The function f(x)= a ●

Page 5: Data Analysis and Regression

This page explores the practical application of quadratic functions in data analysis, specifically focusing on automobile speed and mileage relationships.

Example: A scatter plot of speed versus mileage data is analyzed using quadratic regression.

Highlight: The quadratic regression model y = -0.008199800x² + 0.746113886x + 13.46863137 best fits the data.

Vocabulary: Quadratic regression is used to find the best-fitting parabola for a set of data points.

Section 2.1 Quadratic Functions Definition of a Quadratic Function ● ● ● Let a, b, and c be real numbers with a # 0, The function f(x)= a ●

Page 4: Writing Parabola Equations

This page focuses on constructing quadratic equations given specific conditions, particularly using vertex form.

Definition: The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h,k) is the vertex.

Example: Writing an equation for a parabola with vertex (1,2) passing through (0,0) yields f(x) = -2(x-1)² + 2.

Highlight: The process involves using given points to determine the value of 'a' in vertex form.

Section 2.1 Quadratic Functions Definition of a Quadratic Function ● ● ● Let a, b, and c be real numbers with a # 0, The function f(x)= a ●

Page 1: Introduction to Quadratic Functions

This page introduces the fundamental concepts of quadratic functions and their graphical representations. The standard form and vertex form of quadratic functions are thoroughly explained, along with their key characteristics.

Definition: A quadratic function in standard form is f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.

Highlight: The leading coefficient 'a' determines whether the parabola opens upward (positive a) or downward (negative a).

Vocabulary: The axis of symmetry is a vertical line that divides the parabola into two identical halves.

Example: For f(x) = -2(x - 3)² + 6, the vertex is at (3,6) and the axis of symmetry is x = 3.

Section 2.1 Quadratic Functions Definition of a Quadratic Function ● ● ● Let a, b, and c be real numbers with a # 0, The function f(x)= a ●

Page 2: Finding the Vertex

This page details various methods for finding the vertex of a quadratic function, particularly focusing on functions in standard form and their graphical representations.

Definition: The vertex formula for a quadratic function in standard form is h = -b/(2a), where (h,k) represents the vertex coordinates.

Example: For g(x) = x² + 2x + 1, the vertex is calculated as (-1,0) using the vertex formula.

Highlight: The x-intercepts can be found using the quadratic formula when the function equals zero.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying