Quadratic Functions
What is the vertex of the following parabola:
y=4(x+1)2-3
(-1,-3)
Perform the following polynomial operation:
(3x+2)-(x-3)
2x+5
When identify h, what do we need to remember to do with the sign.
flip the sign.
Identify the domain and range of the graph
Domain (-infinity, infinity)
Range (-infinity, 5]
Find the vertex and axis of symmetry for the following quadratic equation:
f(x)=(x-2)(x-1)
h=3/2 or 1.5
k=1/4 or .25
Write the axis of symmetry for the parabola
y=(x-2)(x+2)
x=0
Simplify the polynomials:
.5(6x-12)+2(2x-1)
7x-8
In your own words how can you tell where a graph in increasing?
When tracing the graph, your pencil moves up.
State the intervals of increasing and decreasing.
Increase:(-infinity, 2)
Decrease: (2, infinity)
Find the vertex and axis of symmetry for the following quadratic function:
f(x)=x2+5x-6
h=-5/2 or -2.5
k=-12.25
Describe the transformation of
y=-3|x+4|-5.
Reflection over the x-axis
Vertical Stretch by 3
Left 4
Down 5
Simplify the polynomials
(3x-2y)-(4x+y)
-1x-3y
How do we read domain?
HINT: ____ to ______
Left to right
Describe the transformation of the parent graph:
Up 5
Right 2
Reflection over the x-axis
Write an equation of the parabola in intercept form that has x-intercepts of -2 and 4 and passes through the point (2,-16).
y=2(x+2)(x-4)
Given the equation y=.5|x+3|, describe the effect the .5 has on the graph.
Vertical Shrinks - this makes the graph of the function wider.
Simplify the polynomials
(4x-1)(x+2)
4x2+7x-2
Reflection over the x-axis.
Write an equation for the function in the graph:
y=-(x-2)2+5
Find the domain and range of this function.
y=|x-4|+1
Domain: (-infinity, infinity)
Range:[1, infinity)
For what value of a does the parabola y=a(x-1)(x+3) have a y-intercept of (0,6).
(x-3)(x2+2x-4)
x3-x2-10x+12
How do you find h and k in intercept form?
h=p+q/2
k=f(h)
Write an equation of the parabola in vertex form that passes through the point (2,-7) and has a vertex of (3,-3).
y=-4(x-3)2-3
Describe the transformations
y=|x-4|+1
Right 4
Up 1