Open Up/Down, Y-Intercept
State whether the parabola opens up or down and find the y-intercept:
y=x2+3x+9
Open up, (0,9)
How many x-Intercepts does the following function have?
y=-2x2+4x+1
Two X-Intercepts
What does the graph of an axis of symmetry, for example the line x=3, look like?
Straight Vertical Line
Once we have find the axis of symmetry, what is the process for finding the vertex?
The value of the axis of symmetry is the x-coordinate. You plug that into the equation for x to solve for the y-coordinate of the vertex.
Solve for x by taking square roots:
2(x-1)2-7=3
x=1+/- sqaureroot(5)
State whether the parabola opens up or down and find the y-intercept:
y=-3x2+7x-5
Open Down, (0,-5)
Find the x-intercepts of the function:
y=2x2-2x-5
(1+sqaureroot(11)/2,0) and (1-sqaureroot(11)/2,0)
What is important about the axis of symmetry?
It is the line across which the parabola is symmetrical, or a mirror image of itself.
Find the vertex of the function:
y=x2+8x+3
(-4,-13)
Solve by factoring (by grouping):
3x2+10x+8=0
x=-4/3, -2
State whether the parabola opens up or down and find the y-intercept:
y=-x2+4
Open Down, (0,4)
Find the X-Intercepts of the function:
y=4x2-5x-6
(-3/4,0) and (2,0)
Find the axis of symmetry for the following function:
y=x2-3x+4
x=3/2
Find the vertex of the function:
y=2x2-2x+4
(1/2,7/2)
x2+6x-3=0
x=-3+/- 2squareroot(3)
State whether the parabola opens up or down and find the y-intercept:
y=2x2
Open Up, (0,0)
Find the x-intercept(s) of the function:
y=4x2-12x+9
(3/2,0)
Find the axis of symmetry of the following function:
y=-4x2+7x-9
x=7/8
Find the vertex of the function:
y=2x2-7
(0,-7)
9x2-6x+1=0
Discriminant=0, One Real Solution
State whether the parabola opens up or down and find the y-intercept:
y=-3x2+2x
Open Down, (0,0)
Give an example of a quadratic function that has no x-intercepts.
-
Find the axis of symmetry of the following function:
y=50x2-500x+1
x=5
What vertical line does the vertex lie on?
The Axis of Symmetry
-2x2+5x+3=0
x=-1/2, 3