Graph Features
What graph feature represents a minimum or maximum?
Vertex
Name the vertex.
f(x) = (x-3)2 + 4
(3,4)
Which part of a quadratic function in standard form is the y-intercept?
c
A pool has dimensions (2x+4)(x-1). Write a quadratic equation in standard form for the area. Then, find the area if x = 6 ft.
f(6)=80 ft2
Which type of function has constant first differences?
Linear
What is the name of a quadratic graph?
Parabola
What is the equation for the axis of symmetry?
f(x)= -3(x+1)2 - 2
x = -1
What is the equation to find the x-value of the vertex?
x = -b/2a
The height of a projectile is modeled by the function
h(t)= -16t2+50t+12.
What is the initial height of the object?
12 ft
Exponential. Common Ratio = 2
How many points do you need to properly graph a parabola?
5
True or False: The graph of g(x)= 0.25x2 is narrower than the parent function f(x)=x2
False.
What is the equation for the line of symmetry?
f(x)= -2x2+20x-5
x=5
The height of a projectile is modeled by the function
h(t)= -16t2+50t+12.
What is the initial velocity of the object?
50 f/s
A function has y-values that increase as shown:
1,4,9,16,25... What type of function models the data?
Quadratic: 2nd difference = +2
What graph feature represents a starting value?
y-intercept
What is the equation of a function that has been translated 3 units right and 2 units down from f(x)=4(x-2)2+5
g(x)=4(x-5)2+3
Find the vertex:
f(x)=2x2-8x+7
(2, -1)
The height of a projectile is modeled by the function
h(t)= -16t2+50t+12.
What is the maximum height of the object?
About 51 feet
Find the quadratic regression equation for the data:
x 1 2 3 4 5
y 15.7 22.8 33.1 46.2 58.5
What is the b value? Round to 3 decimal places.
b=5.243
True or False: Mrs. Halligan loves quadratic functions.
True
Write the equation of a parabola with a vertex of (-3,2) that passes through the point (-5, -2)
f(x)= -(x+3)2+2
Write the equation in standard form:
f(x)= -3(x+4)2-9
f(x)= -3x2-24x-57
The height of a projectile is modeled by the function
h(t)= -16t2+50t+12.
When does the object reach its maximum height?
The average rate of change of a function over the interval 1<x<2 is less than the slope over the interval 2<x<3. What type of function(s) might model the data?
Quadratic or Exponential.