Name _______________________________________________
Algebra 2/Trig - Vertex Form of a Parabola CLASSWORK
Date ______________
Learning Goals: What is vertex form of a parabola and how do we convert from standard form to vertex form
of a parabola?
Do Now:
a) Graph y = x2 using the calculator.
b) Do not erase graph from (a) and now graph
y = x2 + 4x + 9 and y = (x + 2)2 + 5 on the
same set of axes. What do you notice?
c) What transformation of y = x2 is occurring in
part (b)?
As you watch the video, take notes in the space provided. Do not write everything down – choose the important
ideas.
VERTEX FORM OF A PARABOLA
Practice: What transformation of y = x2 is occurring in each of the equations below? Also state the vertex and
the equation of the axis of symmetry.
a) y = (x – 3)2 + 7
b) y = (x + 4)2 – 3
c) y = (x + 2)2
STEPS TO CONVERT A PARABOLA INTO VERTEX FORM
In order to identify the properties of a parabola, we need to convert the equation into its vertex form. In other
words, we want equation (a) to look like equation (b) so we can figure out the vertex of the parabola and the
transformation that is occurring.
a) y = x2 + 4x + 9
b) y = (x + 2)2 + 5
1. Isolate x-terms (move constant to other side)
2. Complete the square on the x-terms
3. Factor the Perfect Square Trinomial
4. Isolate y-variable (move constant back to other side)
5. Now you can identify properties of the parabola
1. Isolate x-terms (move constant to other side)
2. Complete the square on the x-terms
3. Factor the Perfect Square Trinomial
4. Isolate y-variable (move constant back to other side)
5. Now you can identify properties of the parabola
1) Write the equation of the parabola in vertex form, state the vertex, axis of symmetry, and the transformation
that is occurring to y = x2: y = x2 – 6x + 4
2) Write the equation of the parabola in vertex form, state the vertex, axis of symmetry, and the transformation
that is occurring to y = x2: y + 2 = x2 + 8x
1. Isolate x-terms (move constant to other side)
2. Complete the square on the x-terms
3. Factor the Perfect Square Trinomial
4. Isolate y-variable (move constant back to other side)
5. Now you can identify properties of the parabola
3) Write the equation of the parabola in vertex form, state the vertex, axis of symmetry, and the transformation
that is occurring to y = x2: y + 5x = x2 + 1
4. Which equation represents the parabola shown in the accompanying graph?
1)
2)
3)
4)