Name:
Hour:
Date:
Graphing Quadratic Equations from All Forms
Introduction to Solutions of a Quadratic Equation using Tables, Graphs, and Factoring.
CCSS Covered by this activity
A.REI.4b Solve quadratic equations in one variable.
(b) Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the
quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic
formula gives complex solutions and write them as a ± bi for real numbers a and b.
F.IF.8a Write a function defined by an expression in different but equivalent forms to reveal and explain
different properties of the function.
(a) Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values,
and symmetry of the graph, and interpret these in terms of a context.
A.SSE.3a. Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.
(a)Factor a quadratic expression to reveal the zeros of the function it defines.
Name:
Hour:
Date:
Graphing Quadratic Equations from All Forms
Directions: For each of the following equations:
a) Find the y-intercept and x-intercepts by factoring.
b) Create a table of values including all key points and showing how you found the others.
c) Graph using the table of values.
d) Use the graph to write the equation in vertex form (a(x - h)2 + k) and identify the maximum or minimum value
Table 1
Graph of Function 1
Function 1
Vertex:
f(x) = x2 + 4x + 3
x
y
y-intercept:
Factored form:
Vertex Form: a(x-h)2+k
Solutions:
x-intercepts:
Min/Max? Value?
Function 2
f(x) = x2 - 6x + 8
y-intercept:
Factored form:
Table 2
x
Graph of Function 2
y
Vertex:
Vertex Form: a(x-h)2+k
Solutions:
x-intercepts:
Min/Max? Value?
Function 3
f(x) = x2 + 8x + 12
y-intercept:
Table 3
x
Graph of Function 3
y
Vertex:
Factored form:
Vertex Form: a(x-h)2+k
Solutions:
x-intercepts:
Min/Max? Value?
Function 4
f(x) = x2 + 6x + 5
y-intercept:
Factored form:
Solutions:
Table 4
x
Graph of Function 4
y
Vertex:
Vertex Form: a(x-h)2+k
x-intercepts:
Min/Max? Value?
Name:
Hour:
Date:
Graphing Quadratic Equations from All Forms
Use your work above to answer these questions. Write in complete sentences.
1. How is the y-intercept related to the standard form?
2. How do you see the y-intercept in the table?
3. How do you see the vertex in the table?
4. How are the x-intercepts related to the factored form?
5. How do you see the solutions in the table?
6. Suppose you are given the table to the right for the equation y = x2+6x+8.
From the table, identify: solutions, y-intercept, and vertex. Explain how you know for each.
7. Suppose this is a graph you are given for a quadratic equation.
What would be the factored form for the graph? (Each mark is 1
unit).
8. Look at the graph to the right.
a) What is the factored form? _____________________
b) What is the vertex form? ______________________
c) What is the standard form? _____________________
9. Look at the graph to the right.
a) What is the factored form? _____________________
b) What is the vertex form? ______________________
c) What is the standard form? _____________________
X
-5
-4
-3
-2
-1
0
Y
3
0
-1
0
3
8