Quadratic
Is the function y = x2 a quadratic? Why or why not?
Yes this is a quadratic function because the x2 term creates a parabola.
How does the function y = x2 + 1 compare to y = x2 ?
The function shifts up one
How does the function y = (x - 2)2 compare to the function y = x2 ?
The function shifts to the right 2 spaces.
Is the function y = -4x2 facing up or down? How do you know?
Down because the coefficient of x2 is a negative number
What is the vertex of the function y = x2 ?
(0,0)
Is the function y = 2x - x2 a quadratic? Why or why not?
Yes this is a quadratic because the highest exponent is 2 and when graph creates a parabola.
How does the function y = x2 - 10 compare to the function y = x2 ?
The function shifts down 10 units.
How does the function y = (x + 4)2 compare to the function y = x2 ?
The function shifts to the left 4 spaces.
Is the function y = (4/3) x2 facing up or down? How do you know?
Facing up because 4/3 is a positive number
What is the vertex of the function y = x2 + 5?
(0,5)
Is the function y = x2 - x3 + 1 a quadratic? Why or why not?
No this is not a quadratic because the highest term is 3.
How does the function y = (x- 3)2 compare to the function y = x2 ?
The function shifts to the right 3 spaces.
How does the function y = x2 + 8 compare to the function y = x2 ?
The function shifts up 8 units.
Is the function y = x2 -4x - 3 facing up or down? How do you know?
Up because the number in front of x2 is positive
Write the equation for a quadratic function that has been translated 2 units up and 4 units to the left from y = x2 .
y = (x + 4)2 + 2
Yes because this is because 2x2 is a parabola.
How does the function y = (x+ 1)2- 1 compare to the function y = x2 ?
The function shifts down 1 space and to the left 1 space.
How does the function y = (x + 6)2 - 2 compare to the function y = x2 ?
The function shifts to the left 6 and down 2.
Is the function y = 6x - x2 facing up or down? How do you know?
Facing down because number in front of x2 is negative
Write the equation for a quadratic that is translated 2 units down from y = x2 .
y = x2 -2
Yes! This simplifies to y = -x2 which is a quadratic because it creates a parabola.
How does the function y = (x + 0 )2 + 9 compare to the function y = x2 ?
The function shifts up 9 units.
How does the function y = (x - 10)2 - 10 compare to the function y = x2 ?
The function shifts to the right 10 and down 10.
Is the function y = 9 - 5x + (1/2)x2 facing up or down? How do you know?
Up because number in front of x2 term is positive
Create two equations:
1. A quadratic that shifts down 1 and left 3 from y = x2
2. An equation that shifts down 10 right 6 from y = x2
(9,
1. y = (x+3)2- 1
2. y = (x- 6)2- 10