Parabolas
Describe how the graph is related to f(x) = x2: g(x) = x2 + 3
Shifted up 3 units
Solve: -4x + 2x2 + 2 = 13x + 4
-0.1 or 8.6
Determine if the relation is quadratic, linear, or exponential and find an equation to represent it: (0,0); (1, 3); (2, 12); (3; 27); (4, 48)
quadratic, y = 3x2
Graph and state the domain and range: f(x) = |2x-2| + 1
Domain: all real numbers
Range: {y | y ≥ 1}
Describe how the graph is related to f(x) = x2: g(x) = (x-6) 2
It's shifted to the right 6 units
Find the value of x if a rectangle with side lengths x+5 ft and 2x ft has area 110 ft2.
x = 5.3 ft
Determine if the relation is quadratic, linear, or exponential and find an equation to represent it: (-5, 1); (-4, 4); (-3, 7); (-2, 10); (-1, 13); (0, 16)
linear; y = 3x + 16
Graph and state the domain and range:
f(x) = { 2x-3 if x < 1
{ 3x + 4 if x ≥1
Domain: All real numbers
Range: { y | y < -1 or y ≥ 7}
Describe how the graph is related to f(x) = x2: g(x) = -2x2
It's skinnier and upside down
Make an equation and solve: The product of two consecutive odd integers is 257. Find the integers.
-19 and -17 or 17 and 19
Determine if the relation is quadratic, linear, or exponential and find an equation to represent it: (-1, 3); (0, 1); (1, 1/3); (2, 1/9); (3, 1/27)
exponential; y = (1/3)x
Graph and state the domain and range:
f(x) = {-2x + 4 if x < 2
{3x -1 if x ≥ 2
Domain: all real numbers
Range: {y | y > 0 }
Describe how the graph is related to f(x) = x2: g(x) = -(x+1) 2 -2
It's upside down and shifted left 1 unit and down 2 units.
A leaf is floating down to the ground from a height of 25ft. The equation representing its height over time is h = -t2 + 5t + 25. How long will it be in the air before it hits the ground?
8.1 seconds
Determine if the relation is quadratic, linear, or exponential and find an equation to represent it: (-2, -1/2); (-1, 1); (0, -2); (1, 4); (2, -8)
exponential, y = (-2)(-2)x
Graph and state the domain and range: f(x) = -3[[x]]
Domain: All real numbers
Range: All multiples of 3
Describe how the graph is related to f(x) = x2: g(x) = 1/2(x + 3) 2 -4
It's wider, shifted left 3 units and down 4 units.
Find the value of x if the area of a triangle is 20 and the height is x -2 and the base is 2x + 1.
x = 4.8
Determine if the relation is quadratic, linear, or exponential and find an equation to represent it: (4, 10); (6, 7); (8, 4); (10, 1)
Linear; y = -3/2x + 13
Graph and state the domain and range: f(x) = 1/2 [[x]] - 1
Range: All multiples of 1/2