How do you convert a quadratic function from vertex form to standard form?

To convert from vertex form $$f(x) = a(x-h)^2 + k$$ to standard form, expand the equation: $$f(x) = a(x^2 - 2hx + h^2) + k$$ .

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 $$(h, k)$$ is the vertex of the parabola.

How do you find the y-intercept of a quadratic function?

The y-intercept can be found by evaluating the function at $$x = 0$$ , which gives $$f(0) = c$$ in the standard form $$f(x) = ax^2 + bx + c$$ .

What is the relationship between the roots and the vertex of a quadratic function?

The vertex lies on the axis of symmetry, which is equidistant from the roots of the quadratic function. The x-coordinate of the vertex is the average of the roots.

What is the discriminant of a quadratic equation?

The discriminant is given by $$D = b^2 - 4ac$$ and determines the nature of the roots: if $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; if $$D

How do you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, y-intercept, and plot additional points. Then, draw a smooth curve through these points.

What is the effect of changing the value of 'b' in a quadratic function?

Changing the value of 'b' affects the position of the vertex and the axis of symmetry, but does not change the direction of the parabola.

What is the effect of changing the value of 'c' in a quadratic function?

Changing the value of 'c' shifts the graph vertically. It affects the y-intercept but does not change the shape or direction of the parabola.

Properties of Quadratic Functions Flashcard

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a quadratic function?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic function?

Back

3.

FLASHCARD QUESTION

Front

What is the vertex of a quadratic function?

Back

4.

FLASHCARD QUESTION

Front

How do you find the vertex from the standard form?

Back

5.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

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

Back

Create a free account and access millions of resources

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

By signing up, you agree to our Terms of Service & Privacy Policy

Already have an account?

Similar Resources on Wayground

10 questions

English 10 (Final Round)

Flashcard

•

10th Grade

13 questions

7517 03 Basic Operations in Programming Languages

Flashcard

•

9th Grade - University

12 questions

Like to vs Would like to - course 6 (2H)

Flashcard

•

9th - 12th Grade

10 questions

Smart Online Shopper

Flashcard

•

KG - University

12 questions

Legal Writing Memo Flashcard

Flashcard

•

KG - University

12 questions

American Revolution

Flashcard

•

8th - 12th Grade

15 questions

Water Cycle

Flashcard

•

8th Grade - University

15 questions

Understanding SMART Goals Components

Flashcard

•

8th Grade - University

Popular Resources on Wayground

10 questions

Honoring the Significance of Veterans Day

Interactive video

•

6th - 10th Grade

10 questions

Exploring Veterans Day: Facts and Celebrations for Kids

Interactive video

•

6th - 10th Grade

19 questions

Veterans Day

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

15 questions

Circuits, Light Energy, and Forces

Quiz

•

5th Grade

6 questions

FOREST Self-Discipline

Lesson

•

1st - 5th Grade

7 questions

Veteran's Day

Interactive video

•

3rd Grade

20 questions

Weekly Prefix check #2

Quiz

•

4th - 7th Grade

Discover more resources for Mathematics

15 questions

Two Step Equations

Quiz

•

9th Grade

19 questions

Explore Triangle Congruence and Proofs

Quiz

•

9th - 12th Grade

10 questions

Types of Slope

Quiz

•

6th - 9th Grade

10 questions

Exploring the Basics of Ratios

Interactive video

•

6th - 10th Grade

15 questions

Identify Triangle Congruence Criteria

Quiz

•

9th - 12th Grade

23 questions

Similar Figures

Quiz

•

9th - 12th Grade

17 questions

Parallel lines cut by a transversal

Quiz

•

10th Grade

16 questions

Domain and Range of Functions

Quiz

•

9th Grade