Name That Graph
Linear Systems
Linear or Nah?
Quadratic Functions
Misc
100
Find the equation for the parabola in vertex form
y=.17(x-50)^2-7
100
You may use calculators
Round to the nearest tenth
The the x and y intercepts for this inequality:
.5x + 20y > 13
6x +.1y < 54
(0,0.65) (26,0) (0,540) (9,0)
100
Is this linear? What is the equation? Explain
(0,1)
(1,4.5)
(2,20.25)
No, Exponential, y=4.5^x
100
Convert:
y=-2x²-8x+9 to vertex form and find its roots.
y=-2(x+2)²+17
Roots: (4.915,0)(0.915,0)
100
Convert the equation: 5x²+50x-20 into Vertex Form.
No Calculators
Y = 5 ( x + 5 ) ^2 - 145
200
Find the equation for the parabola in vertex form
y=0.556(x-4)^2+3.7
200
Find the point of intersection of this system of linear inequalities
2x + 6y < 13.6
X - y > -10
Round to nearest tenth.
(-5.8, 4.2)
200
Is this linear? Explain
(0,1)
(1,6.5)
(12.545,70)
Linear Y=5.5x+1
200
A soccer coach kicks a ball from a starting height of 0 feet and initial velocity of 64 ft/s. Use the vertical motion model, h=-16t²+vt+s, where v is the initial velocity of ft/s and s is the height in feet to calculate how long the ball will be in the air. Find the vertex and roots and make a table.
Time in air= 4 seconds
Vertex= 64
Roots= (0,0) and (4,0)
Graph= t h
0 0
1 48
2 64
3 48
4 0
200
The opposite side of a right triangle is y = 7x + 9.87. The adjacent side of a right triangle is y = 9.6x + 4.23. If x = 2.76, what is the hypotenuse of the right triangle?
If there is a decimal, round to the nearest hundredth.
Answer: (7*2.76 + 9.87)^2 + (9.6*2.76 + 4.23) = c^2
29.19^2 + 30.726^2= c^2
852.0561 + 944.087076 = 1,796.14318
c = 42.3809294377
300
Find the equation for the parabola in vertex form and round to the nearest thousandth
y=0.123(x+1.321)^2+8
300
You want to buy food for a barbeque. You only have a bag that can fit 12 cubic metres of space. There are two different kinds of food that you can get. Hot dogs and hamburgers. A pack of hamburgers takes up 1.7 metres of space and feeds 5. A pack of Hot Dogs takes up 1 metre of space and feeds 3. The supermarket has only four hamburger packs left. You need to decide how much to buy of each to feed the maximum amount of people while fitting the food in the bag. Round your answer.
Four hamburger packs, 5 hot dog packs
300
Are these points linear or not?Explain.
(6.806, 1.68)
(6.965, 2.756)
(6.972, 2.805)
No, Quadratic
300
Write an equation given the roots and vertex point.
Vertex: (6, 14)
Roots: (-5.602, 0) and (17.602, 0)
y=-0.104(x-6)^2+14
(-5.602,0)(17,602,0)
300
Find the focus and directrix for this parabola.
a = -0.75
No Calculators Allowed
If there is a decimal, round to the nearest
hundredth.
Answer: Focus: (8.125,9.06667) Directrix: y = 9.73333
400
Find the equation for the parabola in vertex form and convert it into standard form
y=9(x-0.9)^2-9
9x^2-16.2x-1.71=y
400
James is preparing his nephew’s birthday party. James is responsible for the balloons. There are two different types of balloons available, dinosaur and non-dinosaur. The dinosaur balloons cost 15 dollars for a pack of 5. The normal balloons cost 8 dollars for a pack of 4. You can only buy 100 dollars worth of balloons. James’ nephew wants as many dinosaur balloons as possible. However, James’ sister wants to have at least ⅓ of the total balloons be normal. James’ wants to buy the most amount of balloons while meeting these requirements. Round if necessary.
5 packs of normal balloons, and 2 packs of dinosaur balloons
400
Linear? Explain
0,1
0.013, 2.454
0.028, 7.015
Exponential
400
Tiffany throws a stone off a bridge into a river below.The stone's height (in meters above the water), x seconds after Alain threw it, is modeled by: h(x)=-5x²+10x+15
Find how many seconds after being thrown the stone will hit the water, graph the parabola, find its roots, and find its vertex.
The stone will hit the water at 3 seconds.
Vertex: (1,20)
Roots: (-1,0)(3,0)
Graph: y-int: (0, 15) Vertex form: y=-5(x-1)²+20
400
Find the two points where the parabola and line intersect.
The vertex - (0,-1)
Point on the parabola - (1,0)
Two points on the line - (-0.667,0) and (1,1)
(-0.18, -0.968) and (1.847, 2.412)
500
Find the equation for the parabola and convert it into standard and back to vertex form
y=7(x-22)^2+3
7x^2-308x+3391
y=7(x-22)^2+3398
500
Solve this problem using only elimination method. Show your work.
The sum of all three digits of a number is 13. Reversing the ones and hundreds digits increases the number by 693. The tens digit plus the ones digit is five less than the hundreds digit. What is the number?
Answer: 229
500
There are two sets of points that make up equations, that intersect at two places, what is the coordinate that is an integer?
1)
(0,1.2)
(0.4,2.12)
(7,18)
2)
(0,2)
(0.4,2.12)
(4,18)
The integer they intersect at is (2,6)
The equations are
1)y=2.4x+1.2
2)y=x^2+2
500
Mendel and Abraham were playing basketball after school. Let h be height in centimeters and t be time in seconds. For Mendel, to find the time it took for his basketball to strike the ground, use h=-10t^2+52t+94. For Abraham, to find the time it took for his basketball to strike the ground, use h=-14t^2+44t+92. Find the time it takes for the basketball to hit the ground, and how high it bounces and what time that’s at. Whose ball bounced higher? Round all decimals up to an integer.
It takes 7 seconds for Mendel’s ball to strike the ground, and it bounces to 160 cm at 3 seconds
It takes 5 seconds for Abraham’s ball to strike the ground, and it bounces to 124 cm at 2 seconds
Mendel’s ball bounced higher
Mendel’s roots= 7, -1
Abraham’s roots= 5, -1
500
Kokwe is playing Around The World. The two points in which the three point line intersects the base line is where she shoots. She also shoots at the top of the key/point. The baseline is the x axis. The court that she shoots at has a full parabola instead of a half parabola with straight sides for their three point line. Two points on the three point line are (2 , -1.141) and (4.75 , 2.54) ← That is the vertex of the parabola. Find the equation for the parabola in both vertex and standard form. Also, find the x & y values (coordinates) of where Kokwe shoots. (include the picture for reference)
Answer: Equation - y = -0.5 (x - 4.75)^2 + 2.54
Where Kokwe shoots: Roots - x = 2.496 & 7.004; Vertex - h = 4.75; k = 2.54
Hint: She shoots at the roots & vertex of the parabola.