Things About Quadratic Functions
Transformations
All Intercepts
Graphing Stuff
Applications
100
What shape is the graph of a quadratic?
parabola
100
y=(x−2)2+5: Describe the transformation for y=x2
Right 2, Up 5
100
How do you find x and y-intercepts of any function? Tell the process for each.
For x intercepts, let y=0 and solve for x
For y intercepts, let x=0 and solve for y.
100
Is the vertex a maximum or minimum for the function
f(x)=-2/3(x+5)^2-9
maximum
100
A ball is thrown upward and can be modeled by the equation h(t)=−16t^2+80t+160 where t=time in seconds and h(t) is the height in feet after t seconds.
What is the initial velocity the ball is thrown with and how far is the person throwing the ball above the ground to start?
velocity: 80 feet per second
initial height: 160 feet
200
What is the point that is the maximum or minimum called on a parabola?
vertex
200
y=−x2: Describe the transformation from y=x2
reflection over the x-axis
200
Find the y-intercept. Write your answer as a point.
y=5x^2-9x+12
(0,12)
200
Find the axis of symmetry for
f(x)=2x^2+3x−5
x=-3/4
200
A ball is thrown upward and can be modeled by the equation h(t)=−16t^2+80t+160 where t=time in seconds and h(t) is the height in feet after t seconds.
How high is the ball after 3 seconds?
256 feet
300
How do you tell if a parabola opens up or down?
by the sign in front of a
300
y=3(x+1)2−2: Describe the transformations from y=x2
Left 1, Up –2, Vertical stretch by 3
300
Find the y-intercept. Write your answer as a point
y=1/3(x-9)^2+10
(0,37)
300
Find the vertex:
h(x)=−2x^2−8x+1
(-2,9)
300
A soccer ball is kicked from the ground upward with an initial velocity of v=32 ft/s. Find the max height the soccer ball reaches.
16 feet
400
Looking at an equation, how do you know it is quadratic?
There is x2 and no x term with a higher exponent.
400
y=1/2(x−4)^2+1
Describe the transformations from y=x2
Right 4, Up 1, Vertical shrink by ½
400
Find the x-intercept(s). Write your answer(s) as point(s).
y=x^2-9
(3,0) and (-3,0)
400
Which is the graph of
f(x)=3(x-4)^2+1
D
400
A baseball hit in the air can be modeled by the equation
h(t)=−16t^2+48t+6
where t=time in seconds and h(t) is feet at time t. How long until the ball hits the ground?
4 seconds
500
How do you find the axis of symmetry?
It is the x-coordinate of the vertex.
500
Use transformations to located the vertex of y=−2(x+3)2+7.
Does the parabola open up or down?
vertex (-3,7)
down
500
Find all intercepts of
y=-2x^2+4x+6
Write your answers as ordered pairs.
(0,6), (3,0), (-1,0)
500
Find the vertex of the graph y = 2(x − 4)(x + 2)
(1, -18)
500
A ball is thrown upward from a platform 24 feet above the ground with an initial velocity of 8 ft/s.
Determine when the ball will hit the ground.
1 second