Describe how the graph is related to f(x) = x2: g(x) = x2 + 3
Translated up 3 units
Solve: -4x + 2x2 + 2 = 13x + 4
\frac{17 \pm \sqrt{305}}{4}
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}
Graph, determine if it has a maximum or minimum, find the vertex, and state the domain and range:
y=x^{2}+4x+6
Minimum
V: (-2, 2)
D: {all real numbers}
R: {y |y >=2}
Joey throws a ball with an initial vertical velocity of 32 ft/s from an initial height of 5 ft. When does the ball reach its maximum height and what is the maximum height?
After 1 second, the ball reaches its maximum height of 21 ft.
Describe how the graph is related to f(x) = x2: g(x) = (x-6) 2
It's translated to the right 6 units
Solve:
2x^2+10x = 110
\frac{-5 \pm \sqrt{245}}{2}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) = -|3x-2| + 4
D: {All real numbers}
R:{y| y <= 4}
Graph, determine if it has a maximum or minimum, find the vertex, and state the domain and range:Graph and state the domain and range:
y=-x^{2}+4x+6
Maximum
V: (2, 10)
D: { all real numbers}
R: { y | y <=10}
A ride starts 60 feet below ground and has an initial vertical velocity of 64 ft/s. When does it reach the maximum height and what is it?
After 2 seconds, the maximum height is 4 ft.
Describe how the graph is related to f(x) = x2: g(x) = -2x2
It's vertically stretched and reflected across the x-axis.
Make an equation and solve: The product of two consecutive odd integers is 323. 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-3 if x < 1
{ 3x + 4 if x ≥1
Domain: All real numbers
Range: { y | y < -1 or y ≥ 7}
Graph, determine if it has a maximum or minimum, find the vertex, and state the domain and range:
y = 3x^2 +3x+1
Minimum
V: (-1/2, 1/4)
D:{all real numbers}
R:
{y | y>= \frac{1}{4}}
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?
\frac{5 + \sqrt{125}}{2}s
Describe how the graph is related to f(x) = x2: g(x) = -(x+1) 2 -2
It's reflected and translated left 1 unit and down 2 units.
Colin is building a deck on the back of his family's house. He has enough lumber for the deck to be 144 sq ft. The length should be 10 ft more than its width. What the dimensions of the deck be?
8 ft by 18 ft
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) = {-2x + 4 if x < 2
{3x -1 if x ≥ 2
Domain: all real numbers
Range: {y | y > 0 }
A ride starts 32 feet below ground and has an initial vertical velocity of 64 ft/s. When does it reach the ground level?
2-sqrt{2} seconds
2 + sqrt{2} seconds
Describe how the graph is related to f(x) = x2: g(x) = 1/2(x + 3) 2 -4
It's vertically compressed, translated 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.
\frac{3 + \sqrt{345}}{4} units
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 + 16
Graph and state the domain and range:
f(x) = {-2x + 4 if x > 2
{3x -1 if 0 ≤ x ≤ 2
{2x + 1 if x < 0
D: {all real numbers}
R:{y | y < 5}
The number of book club members for four consecutive years is shown below. Determine which model best represents the data. Then write a function that models the data. How many members would there be after 10. years?
Time (Years) | Members
0 | 5
1 |10
2 |20
3 |40
4 |80
Exponential
y = 5 *2^x
5,120 members
Find the equation of the absolute value graph.
y\ =\ -2|x+6|+2
Find the equation of the piecewise function from the graph.
f(x) = {3x + 5 if x > 0
{ -1/2x - 2 if x ≤ 0