Characteristics
Are the following functions quadratic?
a. y = 2x2+9x-5
b. y = -4x+3
a. yes
b. No
Order the graphs by width from narrowest to widest.
f(x)=2x2
g(x)= 4x2
g(x), f(x)
Graph & solve:
y=x2+4x+3
x = -3
x = -1
x2-2x-15=0
x= -3
x= 5
Solve using Square Root Method:
x2=-100
No real solutions
Tell whether the following functions open up or down:
a. y = 5x2-12
b. y = -x2+3x-7
c. y+x2=x
a. up
b. down
c. down
Order the graphs by width from narrowest to widest.
f(x) = x2
g(x) = 1/3x2
h(x)= 3x2
h(x), f(x), g(x)
Graph & solve:
y=x2+6x+9
x = -3
Solve by factoring:
x2+10x+25 = 0
x = -5
Solve using Square Root Method
5x2+10=330
x = +/- 8
Find the zeros and the max/min from the graph of y=2x2-4x-6.
x = -1 and x = 3
Min = -8
Compare g(x)= x2+5 with the graph of f(x)=x2
opens up, same width, translates up 5
Solve by graphing:
-4x2=3
No real solutions
Solve by factoring:
2x2 - 2x - 4=0
x = -1
x = 2
Solve using Square Root method:
(x-8)2 = 144
x = 20
x = -4
Find the axis of Symmetry
& Vertex of the following function:
y=3x^2+6x+3
x = -1
(-1, 0)
Compare g(x)= 3x2-1 with the graph of f(x)=x2
opens up, narrower, translates down 1.
x2+5=6x
x = 1
x = 5
Solve by factoring:
3x2-6x=24
x = -2
x = 4
Find the Discriminant to determine the number of solutions; then solve using the quadratic formula:
2x2-2x-4=0
36, 2 real solutions
x = -1
x = 2
Find the domain and range of the following graph:
y = x^2-6x+8
D: {R}
R: y>=-1
Compare g(x)= -1/2x2+3 with the graph of f(x)=x2
Opens down, wider, Translates up 3
Solve by graphing:
-4x2=64 - 32x
x = 4
Solve by factoring:
4x2-36x=-81
x = 4.5
Solve using the quadratic Formula:
(Round to nearest hundredth)
x2-6x=-7
x = 4.41
x = 1.59