Graphing Quadratics
What are the x-intercepts of the function?
y=(x+3)(x-5)
(-3,0) and (5,0)
Solve for m:
m2 - 36 = 0
m=+-6
Solve by factoring:
x2 - 25 = 0
x=5, x=-5
What is the quadratic formula?
-b+-square root of b2 - 4ac / 2a
What is the formula for the discriminant?
b2-4ac
What is the axis of symmetry of the quadratic function?
y=x2+8x-6
x=-4
Solve for x:
-39 + x2 = 13
+-2 root 13
Solve by factoring:
x2 - 27x +50 = 0
x=2, x=25
For what types of quadratic functions can you use the quadratic formula to find solutions?
Any!
If the discriminant of a quadratic function is -4, how many x-intercepts will that function have when graphed?
0/None
How can you determine whether a quadratic function will have a minimum or a maximum without graphing it?
If the "a" value is positive it opens up and has a minimum, and if the "a" value is negative it opens down and has a maximum.
Solve for x:
5(x+1)2 = 20
x=1, x=-3
Solve by factoring:
2x2 + 13x - 7 = 0
x=1/2 , x=-7
Solve using the quadratic formula:
x2 + 6x - 10 = 0
What is the discriminant:
x2 + 3x + 75 = 0
-291
What is the axis of symmetry of the function?
y=3(x+6)(x-12)
x=3
Solve by taking roots (hint: Put into vertex form!):
x2 + 4x + 13 = 0
x = -2+-3i
Solve by factoring:
2x2 -7x +25 = 0
Not factorable! (To solve you would want to use the quadratic formula)
Solve using the quadratic formula:
6x2 - 2x + 5 = 0
(1+-i root 29)/6
What is the discriminant?
Based on this value, how many solutions/x-intercepts will the function have?
3x2 - x - 1 = 0
13, so this function would have 2 x-intercepts
What is the vertex of the following quadratic function?
y=2x2+4x-6
(-1,-8)
What feature of a quadratic function does vertex form give you when graphing?
The Vertex
What feature of a quadratic function does factored form form give you when graphing?
The x-intercepts
What feature of a quadratic function does standard form give you when graphing?
The y-intercept
How many x-intercepts can quadratic functions have?
0,1, or 2