Aim #59: What are the key properties we look for in the graph of a quadratic
function?
Homework: Handout
Do Now: Use your calculator to graph
2
y=x -x-6
Vertex and Axis of Symmetry
The vertex of a parabola is the turning point. This value will either be the
maximum point or minimum point of the graph.
The axis of symmetry of a parabola is a vertical line that passes through the
vertex of the parabola and divides the parabola into two congruent halves. The
x-coordinate of the vertex is the equation of the axis of symmetry of the
parabola. "x = ___"
What is the axis of symmetry for the graph on
the left?
What is the vertex (turning point)?
(-2, -9)
We can also figure out the axis of symmetry from the equation of a quadratic
function.
x=
-b
2a
2
1) a. What is the axis of symmetry of the quadratic y = x - 4x - 5?
b. What is the turning point or vertex?
2) What is the turning point of the parabola formed by the equation
2
y = 2x + 14x + 1?
End Behavior
2
Given a quadratic in the form y = ax + bx + c or
2
y = a(x - h) + k:
- If a > 0 then the parabola opens up, which means the graph has aminimum at the
vertex.
- If a < 0 then the parabola opens down, which means the graph has amaximum at
the vertex.
Use the graphs to fill in the tables and answer the questions:
Graph A
Graph B
Answer these questions based on the work from the previous page:
1. What patterns do you notice in the table of values for eachquadratic?
2. How do we know the x-coordinate of the vertex by looking at the x-intercepts
(or any pair of symmetric points on the graph)?
3. What happens to the y-values as the x-values increase to very largenumbers in
both graphs?
4. What about as the x-values decrease to very small numbers?(In the negative
direction)
5. How can we know whether the graph of a quadratic function will openup or down?
Sum It Up!!
Graphs of quadratics are symmetric about both their axis ofsymmetry or their
vertex. The x-coordinate of the vertex is the average of any two symmetric
points, mainly the x-intercepts.
-When the leading coefficient is positive the graph opens up.
-When the leading coefficient is negative the graph opens down.