Axis of Symmetry
The formula for the axis of symmetry.
What is x=-b/2a?
How do we calculate the x-coordinate of the vertex?
What is x=-b/2a?
What is the domain of any parabola?
What is (-∞,∞)?
How do we know if our graphing pattern will be down or up?
Based on the value of a. If a is negative, the pattern will be down. If a is positive, the pattern will be up.
What is the formula for discriminant?
What is b2-4ac?
How do we represent the axis of symmetry on our graph?
What is a dashed, vertical line?
How do we calculate the y-coordinate of the vertex?
First, find x=-b/2a.
Then, substitute that number into the equation/function.
What is the range of the graph?
(-∞,3]
When we create our pattern, at what point do we begin to count from?
What is the vertex?
What is the maximum number of x-intercepts a parabola can have?
What is 2?
What is the axis of symmetry for the following equation?
f(x)=0.5x2+2x
x=-2
What is the value of "a" if our parabola has a minimum?
State the left end behavior for the following equation.
y=3x2+6
As x->-∞, y->∞
Create the pattern table for the equation
y=x2+3x+9
right up
1 1
2 4
3 9
Calculate the discriminant AND state the number of zeros.
y=x2+3x+2
Discriminant = 1
Since the discriminant is positive, there would be 2 zeros (x-intercepts) on the graph.
What is the axis of symmetry for the following equation?
y=3x2+6
x=0
Give an equation of a parabola that has a maximum.
Answers will vary but can be any function of the form ax2 + bx + c with an "a" value that is negative.
State the range of the graph for the following equation.
y=3x2+6x+2
Hint: You do not need the entire graph. Find the vertex and think about which direction the parabola opens.
[-1,∞)
Create the pattern table for the equation
y=-2x2+3x+5
right down
1 -2
2 -8
3 -18
Calculate the discriminant AND state the number of zeros.
y=3x2+6
Discriminant = -72
Since the discriminant is negative, the graph would have 0 zeros (x-intercepts).
What is the axis of symmetry for the following equation?
y=-2x2+3x+5
x=3/4
Given the equation f(x)=4x2+8x,
find the vertex of the function AND state whether it is a maximum or minimum.
What is (-1,-4) and minimum?
This vertex is a minimum because a=4 is positive so the parabola will open up, making the vertex the lowest point on the graph.
State the left AND right end behavior for the equation
y=-0.5x2+4x+2
Left: As x->-∞, y->-∞
Right: As x->∞, y->-∞
Create the pattern table for the equation
f(x)=0.5x2+2x
right up
1 0.5
2 2
3 4.5
Create the equation of a parabola which will have a discriminant of 0.
Answers will vary. Equations should be written such that b2-4ac=0 and a≠0.