Standard to Factored and Back
Matching Graphs
Features of Quadratics Part 1
Standard 6.4
Quadratics in Context
Quadratics in Context
Features of Quadratics Part 2
100
Put this expression into standard form
2(x+2)(x-3)
2x2-2x-12
100
Name the three types of functions
linear, exponential, quadratic
100
What is this form called?
What is vertex form?
100
Which feature of a quadratic describes the maximum height a ball is thrown.
What is the vertex?
100
For a physics experiment, students throw a ball into the air from the top of a school building. They write the expression −16t2+48t+56 to represent the height, in feet, of the ball t seconds after it is thrown.
Based on this expression, what is the height, in feet, of the school building?
56ft
200
Who has the higher vertex? F(x) or g(x)?
g(x)=-2x2+6x
g(x)
200
Draw a graph the will match this equation
y=(x-3)(x+2)
x-int 3 and -2 and happy face
200
Is this graph concave up or concave down? Is the "a value" of this graph positive or negative?
What is concave down and negative?
200
Which feature of a quadratic best describe f(x)=0.
What is the x-intercept?
200
Factored Form is used to find the X-intercepts
What are the nicknames for x-intercepts? Name at least 2 of them.
solutions, roots zeros
300
The side length of a square is 7x + 3. Which expression represents the area of the square?
D
300
Write an equation to match this graph in standard form. Hint: write it in intercept for then
y=x2-1x-6
300
The domain of any quadratic function is ALWAYSSSS....
What is (-inf, inf)?
300
Which statement is not true?
A.Weekly profits decrease from 0-40 cars per week
B. Maximum profit occurs at 40 cars per week
C. The company does not make a profit when producing 80 custom cars a week
D. Profits decrease between 41- 80 cars per week
A
300
What is the domain?
(-inf, inf)
400
The width of a rectangle is w + 4 and the length of the rectangle is 2w + 3. Which expression represents the area of the rectangle?
A
400
Write an equation in intercept form that represents this graph.
What is (x-3)(x-6)?
400
What is the axis of symmetry of this graph?
What is x=3?
400
Which statements are true about the function y=x2+2x−3? Select THREE!
A. The graph of the function opens up.
B. The graph of the function opens down.
C. The graph of the function has a vertex at (1,0)
D. The graph of the function has a vertex at (−1,−4)
E. The graph of the function has an axis of symmetry of x=−1
A,D,E
400
What is the range?
(-inf, 4]
500
Find the x-intercepts by factoring.
(-6,0) (2,0)
500
Use this table to find the x-int, y-int, and vertex
x-int (-6,0) (2,0)
y-int (0,-12)
vertex(-2,-16)
500
What is the range of this graph?
What is [-9,inf)?
500
A football is kicked into the air. Its height above the ground changes according to the equation y=−16x2+80x+3 where x = time in seconds and
y = height in feet. The ball reaches a height of 67 feet twice: once on the way up and once on the way down. How much time does the ball spend at or above a height of 67 feet? Hint: graph on desmos
3 secs
500
What is the minimum point of the function
f(x) = 2x2 – 16x + 33?
Hint: opposite b over 2a
(4,1)