2.2 b
Writing equations in vertex form
5-1
Using Transformations to Graph
Quadratic Functions
Because the vertex is translated h horizontal
units and k vertical from the origin, the vertex
of the parabola is at (h, k).
Hint: Vertical stretch makes the parabola skinnier.
Vertical compression makes the parabola wider.
Holt Algebra 2
5-1
Using Transformations to Graph
Quadratic Functions
Remember!
If the parabola is moved left, then there will
be a + sign in the parentheses.
If the parabola is moved right, then there will
be a – sign in the parentheses.
Do not switch the sign outside the
parentheses!
Holt Algebra 2
5-1
Using Transformations to Graph
Quadratic Functions
Example 4: Writing Transformed Quadratic Functions
Use the description to write the quadratic
function in vertex form.
The parent function f(x) = x2 is vertically
stretched (skinnier) by a factor of
4
3
and then
translated 2 units left and 5 units down to create
g.
Step 1 Identify how each transformation affects
the constant in vertex form.
4
4
=
a
Vertical stretch by :
3
3
Translation 2 units left: h = –2
Translation 5 units down: k = –5
Holt Algebra 2
5-1
Using Transformations to Graph
Quadratic Functions
Example 4: Writing Transformed Quadratic Functions
Step 2 Write the transformed function.
g(x) = a(x – h)2 + k
=
Vertex form of a quadratic function
(x – (–2))2 + (–5) Substitute
k.
=
(x + 2)2 – 5
g(x) =
(x + 2)2 – 5
Holt Algebra 2
Simplify.
for a, –2 for h, and –5 for
5-1
Using Transformations to Graph
Quadratic Functions
Check It Out! Example 4a
Use the description to write the quadratic
function in vertex form.
The parent function f(x) = x2 is vertically
1
3
compressed (wider) by a factor of and then
translated
2 units right and 4 units down to create g.
Step 1 Identify how each transformation affects
the constant in vertex form.
Vertical compression by
:a=
Translation 2 units right: h = 2
Translation 4 units down: k = –4
Holt Algebra 2
5-1
Using Transformations to Graph
Quadratic Functions
Check It Out! Example 4a Continued
Step 2 Write the transformed function.
g(x) = a(x – h)2 + k
Vertex form of a quadratic function
=
(x – 2)2 + (–4) Substitute
=
(x – 2)2 – 4
g(x) =
(x – 2)2 – 4
Holt Algebra 2
Simplify.
for a, 2 for h, and –4 for k.
5-1
Using Transformations to Graph
Quadratic Functions
Check It Out! Example 4b
Use the description to write the quadratic
function in vertex form.
The parent function f(x) = x2 is reflected across
the x-axis and translated 5 units left and 1 unit
up to create g.
Step 1 Identify how each transformation affects
the constant in vertex form.
Reflected across the x-axis: a is negative
Translation 5 units left: h = –5
Translation 1 unit up: k = 1
Holt Algebra 2
5-1
Using Transformations to Graph
Quadratic Functions
Check It Out! Example 4b Continued
Step 2 Write the transformed function.
g(x) = a(x – h)2 + k
Vertex form of a quadratic function
= –(x –(–5)2 + (1)
Substitute –1 for a, –5 for h,
and 1 for k.
= –(x +5)2 + 1
Simplify.
g(x) = –(x +5)2 + 1
Holt Algebra 2
5-1
Using Transformations to Graph
Quadratic Functions
Lesson Quiz: Part II
2. Using the graph of f(x) = x2 as a guide,
describe the transformations, and then
graph g(x) =
(x + 1)2.
g is f reflected across
x-axis, vertically
compressed by a
factor of , and
translated 1 unit left.
Holt Algebra 2
5-1
Using Transformations to Graph
Quadratic Functions
Lesson Quiz: Part III
3. The parent function f(x) = x2 is vertically
stretched by a factor of 3 and translated 4
units right and 2 units up to create g. Write
g in vertex form.
g(x) = 3(x – 4)2 + 2
Holt Algebra 2