Rate of Increase of a Quadratic Function
Read this topicExplanations 4
- In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position. "Quadrat…
By Iris, Vatsal Ojha, Joshua Siktar
- Rates of increase is a small part of quadratic functions but a very interesting and powerful one. Rates of increase is all about the change of one variable as the other increase…
By Ben Ferrara, Joshua Siktar
- When a line is straight, we can say that its rate of change is constant, that it's the same between any two points on the line. We can see that the straight line doesn't increas…
By Hannah Bonville, Vatsal Ojha, Joshua Siktar
- (Video) Finding the Average Rate of Change Between Two Points on a Quadratic Function by Phil Clark In this video, we learn about rate of change or rate of increase in a quadrat…
By Amy Feraco
Problems 26
- Is the rate of increase from AAA to BBB greater than, less than, or equal to the rate of increase from BBB to CCC?
- Using the points given, what is the rate of increase from aaa to bbb?
- Using the points given, what is the rate of increase from b to c?
- Using the points given, what is the rate of increase from the red point to the green point?
- Let f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=ax2+bx+c be a quadratic. What is the leading coefficient of the polynomial f(x+1)−f(x)f(x+1) - f(x)f(x+1)−f(x)?
- Let f(x)=5x2+bx+cf(x) = 5x^2 + bx + cf(x)=5x2+bx+c be a quadratic with leading coefficient 555. What is the value of the polynomial f(x+1)−2f(x)+f(x−1)f(x+1) - 2f(x) + f(x-1)f(x…
- Let f(x)=5x2+6x+7f(x) = 5x^2 + 6x + 7f(x)=5x2+6x+7 be a quadratic. What is the value of f(x+12)−f(x)f(x)−f(x−4)\frac{f(x+12) - f(x)}{f(x) - f(x-4)}f(x)−f(x−4)f(x+12)−f(x) at x=…
- Let f(x)=5x2+6x+7f(x) = 5x^2 + 6x + 7f(x)=5x2+6x+7 be a quadratic. What is the value of f(x+2)−f(x+1)f(x+1)−f(x)\frac{f(x+2) - f(x+1)}{f(x+1) - f(x)}f(x+1)−f(x)f(x+2)−f(x+1) at…
- Suppose f(x)=ax2+bx+cf(x) = ax^2+bx+cf(x)=ax2+bx+c is a quadratic such that f(x+1)−f(x)=4x+10f(x+1) - f(x) = 4x + 10f(x+1)−f(x)=4x+10 for all xxx, and the minimum value of fff i…
- Suppose f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=ax2+bx+c is a quadratic such that f(0)=1f(0) = 1f(0)=1, f(1)=5f(1) = 5f(1)=5, and f(2)=100f(2) = 100f(2)=100. What is f(−1)f(-1)f(−1)?
- Let x,y,zx,y,zx,y,z be positive real numbers such that y2−x2=9y^2 - x^2 = 9y2−x2=9, z2−y2=11z^2 - y^2 = 11z2−y2=11, and x+y+z=15.x+y+z = 15.x+y+z=15. What is 100x+10y+z?100x+10y…
- Let x,y,zx,y,zx,y,z be positive integers such that y2−x2=99y^2 - x^2 = 99y2−x2=99 and z2−y2=101z^2 - y^2 = 101z2−y2=101. What is yyy? Note: 101101101 is prime. Source: inspired …
- Suppose f(x)=ax2+bx+cf(x) = ax^2+bx+cf(x)=ax2+bx+c is a quadratic such that f(n)f(n)f(n) is an integer for every integer nnn. Among such quadratics, what is the smallest possibl…
- What is the rate of increase between x=0x=0x=0 and x=1x=1x=1 for the function f(x)=2x2+x−1f(x)=2x^2+x-1f(x)=2x2+x−1?
- What is the rate of increase between x=−1x=-1x=−1 and x=1x=1x=1 for the function f(x)=2x2+x−1f(x)=2x^2+x-1f(x)=2x2+x−1?
- What is the rate of increase between x=0x=0x=0 and x=1x=1x=1 for the function f(x)=4x2−3x−2f(x)=4x^2-3x-2f(x)=4x2−3x−2?
- What is the rate of increase between x=−1x=-1x=−1 and x=1x=1x=1 for the function f(x)=4x2−3x−2f(x)=4x^2-3x-2f(x)=4x2−3x−2?
- How many times as large is the red parabola's rate of increase compared to the blue parabola's rate from x=0x=0x=0 to x=1x=1x=1?
- How many times as large is the red parabola's rate of increase compared to the blue parabola's rate from x=−2x=-2x=−2 to x=−1x=-1x=−1?
- How many times as large is the red parabola's rate of increase compared to the blue parabola's rate from x=−2x=-2x=−2 to x=0x=0x=0?
- What is the rate of increase going from Point A to Point B?
- Which rate of increase would be the largest?
- Which rate of increase (ROI) is the smallest?
- Which rate of increase is the smallest?
- Which rate of increase is the largest?
- What is the rate of increase from 333 to 555 in the function: f(x)=2x2+3x−6f(x) = 2x^2 + 3x - 6f(x)=2x2+3x−6