Quadratics
Applied Quadratics/Cubics
Quadratic Regression
Direct/Inverse Variation
Inverses
100
The general form of a quadratic equation.
What is ax2+bx+c?
100
According to your notes, these disciplines frequently use mathematical models.
What are physics, engineering, and social sciences?
100
The minimum number of points needed to use a quadratic regression.
What are three points?
100
In direct variation, when the value of one variable increases, the value of the other variable ___________.
Increases.
100
The domain consists of these.
The range consists of these.
What are all possible x-values?
What are all possible y-values?
200
The y-intercept of x2-14x-2.
What is (0,2)?
200
The maximum volume of a box given the function V(x)=3x3-27x2+36x, where x is the size of the cutouts on each corner and V(x) is the volume.
What is 13.1cm3?
200
Generally speaking, using the quadratic regression function on our calculators tells us this about the given points.
The equation of the quadratic that best fits the given points.
200
In a lottery draw, the amount of money m (in $) awarded to each winner varies inversely with the number of winners w. If there are 20 winners, each receives $150.
Write an equation for m in terms of w.
m=3000/w
200
According to your notes, inverse functions have this relationship to one another.
What is undoing/reversing each other?
300
The number of roots in the equation y=3x2+4x+1.
What are two?
300
The maximum height achieved by a ball modeled by the function f(x)=-0.06x2+1.2x, where x is the horizontal distance and f(x) is the height of the ball.
What is 6m?
300
The equation of the quadratic containing the points: (-10, 100), (3, 9), and (19, 361).
What is y=x2?
300
The distance, d meters, that a ball rolls down a slope varies directly with the square of the time it has been rolling for, t seconds. In 2 seconds the ball rolls 9 meters.
Write an equation for d in terms of t.
d=1.5t2
300
Inverse functions are reflected over this line.
What is the line y=x?
400
The value of roots in the equation y=3x2+4x+1.
What is x=-1; -1/3?
400
A soccer player kicks a ball from the goal line and the path is modeled by the function f(x)=-0.06x2+1.2x, where x is the horizontal distance and f(x) is the height of the ball. What are the roots and what does each value represent?
Roots: x=0; 20
0 represents the starting position of the ball and 20 represents the distance traveled by the ball after kicking it.
400
Given this set of data, find the best fitting quadratic model for the data:
Angle: {20, 30, 40, 50, 60, 70}
Distance: {362, 467, 519, 500, 417, 333}
y=-0.265x2+23.0x+13.7
400
The volume V of a sphere varies directly with the cube of its radius r. A certain sphere has radius 3 cm and volume 113.1 cm3.
a) Write an equation for V in terms of r.
b) Find the volume of another sphere with radius 5 cm.
a) V=4.19r3
b) V=524cm3
400
What happens to the domain and range across inverse functions?
The domain and range are switched.
500
The path of a missile through the air can be modelled by the equation h(x) = −0.0007944x2 + 1.251x +20, where x represents the horizontal distance traveled by the missile in metres, and h(x) represents the height of the missile above the ground in metres. Find the maximum height reached by the missile.
What is 513m?
500
A dolphin jumps out of the water and its motion follows the shape of a parabola. The dolphin reaches its maximum height at 0.9 seconds after leaving the water. When will it return to the water?
1.8s
500
The equation of the quadratic function f(x) that has a vertex at (0.375, 11.7) and passes through the point (-2, 23).
What is f(x)=2x2-1.5x+12?
500
a) C=732r3
b) $974
500
Evaluate f(f-1(5))
What is 5?