Parabolas
Solving Quadratics
Lin, Quad, and Exp
Piecewise Functions
Graphing Quadratics
Projectile Motion
100
Describe how the graph is related to f(x) = x2: g(x) = x2 + 3
Translated up 3 units
100
Solve: -4x + 2x2 + 2 = 13x + 4
\frac{17 \pm \sqrt{305}}{4}
100
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
100
Graph and state the domain and range: f(x) = |2x-2| + 1
Domain: all real numbers
Range: {y | y ≥ 1}
100
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}
100
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.
200
Describe how the graph is related to f(x) = x2: g(x) = (x-6) 2
It's translated to the right 6 units
200
Solve:
2x^2+10x = 110
\frac{-5 \pm \sqrt{245}}{2}ft
200
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
200
Graph and state the domain and range:
f(x) = -|3x-2| + 4
D: {All real numbers}
R:{y| y <= 4}
200
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}
200
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.
300
Describe how the graph is related to f(x) = x2: g(x) = -2x2
It's vertically stretched and reflected across the x-axis.
300
Make an equation and solve: The product of two consecutive odd integers is 323. Find the integers.
-19 and -17 or 17 and 19
300
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
300
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}
300
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}}
300
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
400
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.
400
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
400
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
400
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 }
400
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
500
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.
500
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
500
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
500
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}
600
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
600
Find the equation of the absolute value graph.
y\ =\ -2|x+6|+2
700
Find the equation of the piecewise function from the graph.
f(x) = {3x + 5 if x > 0
{ -1/2x - 2 if x ≤ 0