F.IF.8a: Identify Characteristics of Quadratics
F.IF.8a: Identify Characteristics of Quadratics
8. 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.
Overview of Lesson
- activate prior knowledge
- present vocabulary and/or big ideas associated with the lesson
- connect assessment practices with curriculum
- model an assessment problem and solution strategy
- facilitate guided practice of student activity
Optional: Provide or allow students to create additional problem sets
- facilitate a summary and share out of student work
Optional HW - Write the math assignment.
Big Ideas
The graph of a quadratic equation is called a parabola.
 The coordinates of the point
where the parabola crosses the xaxis on a coordinate plane are
known as the x-intercepts..
o The x-intercept occurs
when
y  0 or f  x   0
root
root
vertex (turning
point)
axis of
symmetry
 A quadratic equation
can have one, two, or
zero x-intercepts.
 The equation of the axis of
symmetry is
b
x
2a
 The vertex is found by finding f(x)
at the axis of symmetry
 The value of the independent variable (x) at the x-intercept of a quadratic equation is also known
as the root and/or the solution of the equation.
o Roots, solutions, and zeros have same meanings when working with quadratics.
o Roots and factors have different meanings when working with quadratics.
 Assume that a root of the above parabola is
1
x
2
 The corresponding factor for this root is the left expression of the following
equation
1

x 0
2

REGENTS PROBLEMS
1. The zeros of the function
a.
and 5
b.
and 7
are
c.
d.
and 2
and 3
2. a) Given the function
, state whether the vertex represents a maximum or minimum point for
the function. Explain your answer.
b) Rewrite f(x) in vertex form by completing the square.
F.IF.8a: Identify Characteristics of Quadratics
Answer Section
1. ANS: D
Strategy: Use root operations to solve
for
PTS: 2
REF: 081418a1
NAT: F.IF.8a
2. ANS:
a) The vertex represents a maximum since
.
b)
PTS: 4
REF: 011536a1
NAT: F.IF.8a
.
TOP: Zeros of Polynomials
TOP: Graphing Quadratic Functions