8.1
What does the a variable do to the parabola's?
(Hint: there are 4 answers)
When 0 < a < 1 the parabola opens up and is wider
When a > 1 the parabola opens up and is narrower
When -1 < a < 0 the parabola opens down and is wider
When a < -1 the parabola opens down and is narrower
What does the c variable do to parabola's
c shifts the parabola's up an down
What is the formula to find the axis of symmetry?
-b/2a
Tell whether the points represent a linear, an exponential, or a quadratic function.
(− 2, − 1), (− 1, 0), (1, 2), (2, 3), (0, 1)
Linear
An electric train is heading north, what direction is the smoke going?
There is no smoke its an electric train
Graph the function y =3/4x2. Compare the graph to the graph of y = x2.
This graph should be wider with the points of (0,0)(-2,3)(2,3)
Graph the function y = x2 − 3. Compare the graph to the graph of y = x2.
This graph should shift down 3 units with the points of (0,-3)(-1,-2)(1,-2)
Find the axis of symmetry and the vertex of the graph of the function.
y = −8x 2 − 16x − 1
Axis of symmetry: x=-1
Vertex: (-1,7)
Tell whether the points represent a linear, an exponential, or a quadratic function.
(1, 8), (− 4, 1/4) , (− 3, 1/2) , (− 2, 1), (− 1, 2)
Exponential
There is a cowboy that goes into town on Friday. He stays for three days and leaves on Friday. How can this be?
His horses name is Friday
Graph the function y = 8x2. Compare the graph to the graph of y = x2.
This graph should be narrower with the points of (0,0)(-1,8)(1,8)
Graph the function y = − 2x2 − 1. Compare the graph to the graph of y = x2.
This graph should open down, be narrow, and shift down one unit with the points of (0,-1)(-1,-3)(1,-3)
Describe the domain and range
y = 4x2 + 24x + 31
Domain: all real numbers
Range: y≥-5
Tell whether the data values represent a linear, an exponential, or a quadratic function. Then write an equation for the function using the form y = mx + b, y = abx, or y = ax2.
(− 2, 8), (− 1, 2), (0, 0), (1, 2), (2, 8)
Quadratic: y = 2x2
How can you make the number 7 even without addition, subtraction, multiplication, or division?
Take off the "s" in seven
Graph the function y = − 7x2. Compare the graph to the graph of y = x2.
This graph should open down and be narrow with the points of (0,0)(-1,-7)(1,-7)
Describe how to translate the graph of y = x2 + 2 to the graph of the given function.
y = x2 − 1
The parabola has to shift down 3
Tell whether the function has a minimum value or a maximum value. Then find the value.
y = − 5x 2 + 10x + 7
Maximum: 12
Tell whether the data values represent a linear, an exponential, or a quadratic function. Then write an equation for the function using the form y = mx + b, y = abx, or y = ax2.
(-2,4)(-1,1)(0,-2)(1,-5)(2,-8)
Linear: y = -3x - 2
While a cat was outside, it started to downpour. The cat couldn’t find any shelter and got completely soaked by the rain, yet not a single hair was wet. How could this be?
It was a hairless cat
The cross section of a spotlight can be modeled by the graph of y = 0.5x2, where x and y are measured in inches and –2 ≤ x ≤ 2.
Find the width and depth of the spotlight.
Width: 4 inches
Depth: 2 inches
The function y = − 16x2 + 36 gives the height y (in feet) of an apple after falling x seconds. When does the apple hit the ground?
The apple hits the ground after 1.5 seconds
The function y=-16t2+128t represents the height h (in feet) of a firework t seconds after it is launched. The firework explodes at its highest point.
When does the firework explode?
4 seconds after it is launched
The listed points show the number of people attending the first five football games at a high school.
(1,252)(2,325)(3,270)(4,249)(5,310)
Does a linear, an exponential, or a quadratic function represent this situation?
No none of them fit
What has six faces, but does not wear makeup, has 21 eyes, but cannot see?
A dice