Vocabulary
What is the name for a U-shaped graph of the quadratic equation?
Parabola
What can the sign of the coefficient of an "a" term tell you about the behavior of the parabola? f(x)= ax2 +bx + c
The 'a' term tells you whether the parabola is opens upward or downward.
What does the axis of symmetry do visually?
The axis of symmetry cuts the parabola in half.
Graph the following function: f(x)=(x+2)2+1
Determine the AOS, Vertex, and if the Vertex is a Max or Min.
AOS:x=-2
Vertex:(-2,1)
Min
What do we call the highest or lowest point on a parabola?
Vertex
Where is the y-intercept located? How does this coordinate point look ( , )?
The point where the parabola crosses through the y-axis. (0,#)
What is the formula for the axis of symmetry give the quadratic equation is in Standard Form?
x=-b/2a
Graph the following Function: f(x)=2x2-4x-3
Determine the AOS, Vertex, and if the Vertex is a Max or Min.
AOS:x=-1
Vertex:(-1,3)
Min
What is the name of the form for this quadratic equation? f(x) = ax2 +bx + c
Standard form
Name the x-intercepts. Give points where the parabola is crossing the x-axis. f(x)=1/2(x)(x-2)
(0,0) and (2,0)
What is the axis of symmetry for this quadratic function? f(x)=x2 + 4x + 4
x=-2
Graph the following Function: g(x)=-(x-3)(x-7)
Determine the AOS, Vertex, and if the Vertex is a Max or Min and the X-intercept(s).
AOS:x=5
Vertex:(5,4)
Max
X-Intercept(s): (3,0) and (7,0)
When the vertex is in the lowest part of the parabola, what is it called?
The minimum
What can the coefficient of an "a" term tell you about the behavior of the parabola? f(x)=ax2 +bx + c
'a' being a whole number makes the parabola stretch (narrower). 'a' being a fraction/decimal makes the parabola shrink (wider)
What is the axis of symmetry for this quadratic function? y=-6x2 -6x +9
x=-1/2
Write an equation of the parabola in Vertex form with a Vertex:(5,2) and through the point (1,10)
f(x)=1/2(x-5)2+2
How do we call the line that runs through the vertex and divides the parabola in half.
Axis of symmetry
Name at least 3 steps that you need to take to graph the quadratic function in X-Intercept form.
1. Set y equal to 0.
2.Set each factor with x equal to zero and solve for x.
3. Plot the X-intercepts.
4. Find the location of the vertex by taking the average of the X-intercepts and plugging in this value to obtain the y value of the vertex.
5. Connect the dots
What is the axis of symmetry for this quadratic function? f(x)=-7x2-21x+33
x = -3/2
Write an equation of the parabola in Intercept Form with x-intercepts of -4 and 6, and through the point(-2,32).
f(x)=-2(x+4)(x-6)