Algebra 1
Quadratics #5: Vertex
Name ______________________________
1. Recall your knowledge on finding the line of symmetry of a quadratic function.
a. If given a quadratic equation in standard form, y=ax2 + bx + c, then what is the equation for
the line of symmetry? Be sure to write the equation.
b. Why do we call this line the “line of symmetry for a quadratic function”? What is
symmetrical about a quadratic graph?
2. Using your equation from #1a find the line of symmetry (LOS) of the
following quadratic equation. Be sure that you write it as an equation.
y = x2 – 6x + 3
LOS:
a. Using a blue pencil, draw the line of symmetry on the graph.
b. While showing work, fill in the following table AND then graph
these points on your graph.
X
Y
0
1
2
3
c. Using what you know about the “symmetrical” qualities of a quadratic graph, draw three
more points on your graph. Do not plug in values for x, instead use the line of symmetry to
find new points. Once you have a total of 7 point on the graph, draw your curve.
3. You will recall the “U” shaped graph of a quadratic is called a parabola.
a. Describe in your own words what the “vertex” of a parabola is.
b. Describe any relationship between the vertex and the line of symmetry.
c. Circle the vertex on your graph in #2 with red pencil. And write the coordinates here: (
d. Circle which of the coordinates (x or y) you get from the line of symmetry. Why?
e. Given the x-coordinate how could we find the y-coordinate using the equation?
,
)
4. Given the new quadratic equation: y = 2x2 + 4x – 1.
a. Write the equation for the line of symmetry.
b. You should now know the x-coordinate of the vertex.
Write it here:
(
,
)
c. Using your x-value you should be able to use the equation to find
the y-coordinate of the vertex. Find it, show work below.
X
Y
d. Mark the vertex in red on the given coordinate grid.
e. Pick a couple x-values to the right of your vertex and fill in the
following table. Graph these points on your graph. (show work)
f. Using the symmetrical qualities of the graph find a couple points
to the left of the line of symmetry. Then draw in your parabola.
5. For the following quadratic give 1) find the line of symmetry, 2) find
the vertex (show work for y-coordinate), 3) fill in the table for two
points on the right-hand side of the graph, 4) plot additional points on
the left-hand side of the graph and 5) then graph the parabola.
y = -x2 – 2x + 4
Equation:
1) LOS:
3) Table:
2) Vertex:
X
Y
6. For the following quadratics find the equation for the line of symmetry and the
coordinate pair (x, y) of the vertex. Show work for finding the y-coordinate.
a.
y = x2 – 10x + 3
b.
y = 3x2 + 6x – 2
c.
y = -2x2 + 8x – 1
d.
y = x2 – 2x + 4
e.
y = -x2 - 12x + 5
f.
y = -2x2 + 3x – 6