3.2a Quadratic Functions in Standard Form
https://www.youtube.com/watch?v=lbMir1UAO4I
Quadratic Functions produce graphs called parabolas
It's equation comes in two forms:
1) Vertex Form
2) Standard Form
y = a(x - p)2 + q
y = ax2 + bx + c
**Quadratic Functions have a degree of 2
Ex. Which of the following are quadratic functions:
a)
y = 3x2 - 7x + 3
b)
y = x2 + √x
c)
y = x(x-5)
d)
e)
y = 4x2 - 9x + 12
y = (x + 2)2 - 7
f)
y = x3- 2x2 + 3
g)
y = x2 - 5x + 2x
Ex. Convert the following to standard form
a)
y = (x - 3)2 + 7
Ch3-Quadratic Functions Page 1
b)
y = -2(x + 1)2 -3
Comparing Vertex Form and Standard Form
Vertex Form:
y = a(x - p)2 + q
Ex. Given y = 3x2 - 12x + 5 , determine the vertex if the x-coordinate is given by x =
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Ex. Sketch
y = 2x2 - 12x + 10
by using a table of values. State its properties.
Vertex:
Axis of Symmetry:
Domain:
Range:
Max/min:
x-intercept(s):
y-intercept:
Ex. How many x-intercepts does a quadratic function with:
a) a vertex of (-4,0) that passes through (0,3) have?
b) a maximum of -3 have?
Ex. Given the graph below, determine the domain and range
Assignment: Sec. 3.2a p174 #1,2ac,3,4ac,6-8,16*
Benefits of Vertex Form vs. Standard Form
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Vertex Form
Can read
vertex
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Standard Form
Can read
"a"
in both
Can read
y-intercept