<meta http-equiv="refresh" content="1; url=/nojavascript/">
Skip Navigation

Graphs of Quadratic Functions

Intercepts, vertex, axis of symmetry, and forms of a quadratic.

Atoms Practice
Practice Graphs of Quadratic Functions
Practice Now
Solving and Graphing Quadratic Functions

Feel free to modify and personalize this study guide by clicking “Customize.”


Fill in the empty boxes.

Word Definition
___________ The characteristic shape of a quadratic function graph, resembling a bowl or the silhouette of a bell
Vertex ______________________________________________________________
Quadratic Form ______________________________________________________________
___________ f(x)=ax^{2}+bx+c
Standard Form ______________________________________________________________

excellent for finding -intercepts, is: f(x)=a(x-r_{1})(x-r_{2})

Factoring Polynomials

Choose a name for each method to help you remember. Also, fill in any blanks.
Method Equation Example Steps
________________________ 2x^4-x^2-15

ac = -30

& 2x^4-x^2-15\\& 2x^4-6x^2+5x^2-15\\& 2x^2(x^2-3)+5(x^2-3)\\& (x^2-3)(2x^2+5)

________________________ 81x^4-16 

Difference of squares: & 81x^4-16\\& (9x^2-4)(9x^2+4)

Factor 9x^2-4 with difference of squares also:



________________________  6x^5-51x^3-27x = 0

Pull out Greatest Common Factor:


Use a combination of the first two methods to factor the rest:


Click here for answers.

 Pull out the Greatest Common Factor if there is one!

Graphing Quadratic Functions

Complete the following table.

Form Equation Used For
___________ f(x)=ax^{2}+bx+c ________________________
Vertex Form ________________________ ________________________
___________ ________________________

finding -intercepts

Answer the following questions:
  1. Which letter of which form is the y-intercept? _____________________
  2. Where is the vertex in vertex form_____________________
  3. How do you find the vertex in standard form_____________________
  4. What is the axis of symmetry and how do you find it from standard form_____________________


Factor the following completely:
  1. x^4-4x^2-45
  2. 4x^4-11x^2-3
  3. 16x^4-1
  4. 6x^5+26x^3-20x
  5. 625-81x^4
Answer the following questions:
  1. Which direction does a parabola open if the leading coefficient ( ) is negative?

  2. Consider the quadratic functionsy = 4x^2    y = 5x^2    y = 7x^2 Which quadratic function would you expect to have the widest parabola? Explain your answer.

Sketch the graph of each function:
  1. y = -x^2 + 7
  2. y = 3x^2 + 6x +1
  3. y = \frac{1}{2} x^2 + 2x +4
  4. y = (x + 6)^2 - 3
  5. y = -x^2 -8x -17

Click here for answers.

Image Attributions


Please wait...
Please wait...

Original text