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
\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) = 2 |x| -5
Domain: {all real numbers}
Range: { y | y ≥ -5}
Graph and state the domain and range:
y=x^{2}+4x+6
D: {all real numbers}
R: {y |y >=2}
Describe how the graph is related to f(x) = x2: g(x) = (x-6) 2
It's shifted to the right 6 units
Solve:
2x^2 + 10x = 110
\frac{-5 \pm 7 \sqrt{5}}{2}
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) = -3|x-2| + 4
D: {All real numbers}
R:{y| y <= 4}
Graph and state the domain and range:
y=-x^{2}+4x+6
D: { all real numbers}
R: { y | y <=10}
Describe how the graph is related to f(x) = x2: g(x) = -2x2
It's skinnier and upside down
Solve:
x^2 + 2x = 143
-13 and 11
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) = 2|x-1| + 1
Domain: all real numbers
Range: {y | y ≥ 1}
Graph by making a table with at least 5 points. State the domain and range.
y = 3x^2 +3x+6
D:{all real numbers}
R:
{y | y>= 5 \frac{1}{4}}
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?
\frac{5 + 5\sqrt{5}}{2}s
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
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.
\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