Graphing Quadratic Functions

Graphing Quadratic Functions

Learn how to graph a Quadratic Functions in the vertex or standard forms following few simple steps.

Step by step guide to Graphing Quadratic Functions

  • Quadratic functions in vertex form: \(y=a(x – h)^2+k\) where \((h,k)\) is the vertex of the function. The axis of symmetry is \(x=h\)
  • Quadratic functions in standard form: \(y=ax^2+bx+c\) where \(x=-\frac{b}{2a}\) is the value of \(x\) in the vertex of the function.
  • To graph a quadratic function, first find the vertex, then substitute some values for \(x\) and solve for \(y\).

Example 1:

Sketch the graph of \(y=(x+1)^2-2\).

Solution:

First, recall that a Quadratic function in vertex form is \(y=a(x – h)^2+k\) where \((h,k)\) is the vertex of the function. The vertex of \(y=(x+1)^2-2\) is \((-1,-2)\). Substitute zero for \(x\) and solve for \(y\). \(y=(0+1)^2-2=-1\). The \(y\) Intercept is \((0,-1)\).
Now, you can simply graph the quadratic function.

Example 2:

Sketch the graph of \(y=3(x+1)^2+2\).

Solution:

The vertex of \(3(x+1)^2+2\) is \((-1,2)\). Substitute zero for \(x\) and solve for \(y\). \(y=3(0+1)^2+2=5\). The \(y\) Intercept is \((0,5)\).
Now, you can simply graph the quadratic function.

Exercises

Sketch the graph of each function. Identify the vertex and axis of symmetry.

  • \(\color{blue}{y = 3(x-5)^2-2}\)
  • \(\color{blue}{y=x^2-3x+15}\)

Download Graphing Quadratic Functions Worksheet

  • \(\color{blue}{y = 3(x-5)^2-2}\)
  • \(\color{blue}{y=x^2-3x+15}\)

Related to "Graphing Quadratic Functions"

SBAC Math Grade 7 Practice Test Questions
SBAC Math Grade 7 Practice Test Questions
PSSA Math Grade 7 Practice Test Questions
PSSA Math Grade 7 Practice Test Questions
Top 10 Grade 4 PARCC Math Practice Questions
Top 10 Grade 4 PARCC Math Practice Questions
MCAS Grade 3 Math FREE Sample Practice Questions
MCAS Grade 3 Math FREE Sample Practice Questions
Grade 3 MEAP Math Worksheets
Grade 3 MEAP Math Worksheets
FREE Grade 8 PARCC Math Practice Test
FREE Grade 8 PARCC Math Practice Test
ACT Aspire Math Grade 7 Practice Test Questions
ACT Aspire Math Grade 7 Practice Test Questions
Top 10 Grade 4 ACT Aspire Math Practice Questions
Top 10 Grade 4 ACT Aspire Math Practice Questions
PARCC Grade 3 Math FREE Sample Practice Questions
PARCC Grade 3 Math FREE Sample Practice Questions
Grade 3 ACT Aspire Math Worksheets
Grade 3 ACT Aspire Math Worksheets

Leave a Reply

Your email address will not be published. Required fields are marked *

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…