2. ESSENTIAL UNDERSTANDING AND
OBJECTIVES
Essential Understanding: y = ax2 + bx + c, a, b,
and c provide key information about its graph
Objectives:
Students will be able to:
Graph quadratic equations
Identify the vertex, axis of symmetry, minimum and
maximum from standard form.
3. IOWA CORE CURRICULUM
Algebra
A.CED.2. Create equations in two or more variables to represent
relationships between quantities; graph equations on coordinate axes
with labels and scales.
F.IF.4. For a function that models a relationship between two quantities,
interpret key features of graphs and tables in terms of the quantities, and
sketch graphs showing key features given a verbal description of the
relationship.
F.IF.6. Calculate and interpret the average rate of change of a function
(presented symbolically or as a table) over a specified interval. Estimate
the rate of change from a graph.
F.IF.7. Graph functions expressed symbolically, and show features of the
graph, by hand in simple cases and using technology for more
complicated cases.
F.IF.8. Write a function defined by an expression in different but
equivalent forms to reveal and explain different properties of the function.
F.IF.9. Compare properties of two functions each represented in a
different way (algebraically, graphically, numerically in tables, or by
verbal descriptions)
F.BF.1. Write a function that describes a relationship between two
quantities.
4. REVIEW
What is vertex form for a quadratic equation?
Standard Form: y = ax2 + bx + c
How do you think we switch from vertex form to
standard form?
Put each of the following equations in standard form.
y = (x – 3)2 + 2
y = (x + 4)2 – 1
y = -(x – 1)2 + 5
y = 3(x + 2)2 + 7
How do you think we determine the vertex of an
equation in standard form?
5. PROPERTIES
Change the vertex form to standard form:
a(x-h)2 + k
a=a
b = -2ah
c = ah2 +k
Solve the above for h and k
6. STANDARD TO VERTEX FORM
Convert from Standard form to vertex form
y = 2x2 + 10x + 7
y = -x2 + 4x – 5
7. PROPERTIES
Without a calculator:
The graph f(x) = ax2 + bx + c is parabola
If a > 0, it opens up
If a < 0, it opens down
Axis of symmetry: x = -b/(2a)
Vertex
X = -b/(2a)
Y = f(-b/(2a))
Y – intercept (0, C)
8. WITHOUT THE CALCULATOR
Without graphing find the vertex, axis of
symmetry, min/max value, y intercept, using the
properties of quadratic functions.
Then Graph the function by hand
y = x2 + 2x + 3
y = -2x2 + 2x – 5
y= 2x2 + 5
9. EXAMPLES
Using the calculator, graph y = 2x2 + 8x – 2
Identify the vertex, minimum/max, and the axis of
symmetry, the domain, and the range
Using the calculator, graph y = -3x2 – 4x +6
Identify the vertex, minimum/max, and the axis of
symmetry, the domain, and the range
10. INTERPRETING A QUADRATIC GRAPH
Where in real life do you see parabolas?
The Zhaozhou Bridge in China is the oldest arch bridge,
dating to A.D. 605. You can model the arch with the
function
f(x) = -0.001075x2 + 0.131148x, where x and y are in
feet. How high is the bridge
above its supports?
Why does the model not
have a constant term?
