U4 - Quadratic Functions and Equations

Solve the system of equations. y=2x^2-3 y=3x-1

(-1/2,-5/2), (2,5)

What are the coordinatess of the vertex of the graph of the function y=-3x^2-12x+3?

(-2,15)

What are the coordinates of the vertex of the graph of the function y=-x^2+6x=11?

(3,-2)

Use the quadratic fourmula to solve the equation. If necessary, round to the nearest hundredth. x^2+3=-4x

-1, -3

Solve the equation by completing the square. x^2+9x-14=0

-10.35, 1.35

Solve the equation by completing the square. If necessary, round to the nearest hundredth. x^2-18x=19

-1; 19

Solve the equation by completing the square. Round to the nearest hundredth. x^2+6x=-7

-4.41, -1.59

Solve by factoring. n^2+2n-24=0

-6,4

Solve by factoring. m^2+8m+7=0

-7,-1

Solve. x^2-81=0

-9, 9

How many real number number solutions are there to the equation 0=-3x^2+x-4?

0

The perimeter of a rectangular is 54 cm. The area of the same rectangle is 176 cm^2. What are the dimensions of the rectangle?

11 cm by 16 cm

Solve. x^2-121=0

11,-11

A community group is planning the expansion of a square flower garden in a city park. If each side of the original garden is increased by 3 meters, the new total area of the garden will be 225 square meters. Find the length of each side of the original garden.

12 m

What is the value of 'c' so that x^2-11x+c is a perfect-sqaure trinomial?

121/4

What is the side length of a square with an area of 144x^2?

12x

A model rocket is launched from a roof into a large field. The path of the rocket can modeled by the equation y=-0.06x^2+9.6x+5.4 where 'x' is the horizontal distance, in meters, from the starting point on the roof and 'y' is the height, in meters, of the rocket above the ground. How far horizontally from its staring point will the rocket land? Round your answer to the nearest hundredth.

160.56 m

How many solutions are there for 5x^2+7x-4=0?

2

Solve the equation using the Zero Product Property. (2x-4)(2x-1)=0

2, 1/2

What is the value of 'z' so that -9 and 9 are both solutions of x^2+z=103?

22

A ball is thrown into the air with an initial upward velocity of 46 ft/s. Its height (h) in feet after t seconds is given by the function h=-16t^2+46t+6. After how many seconds will the ball hit the ground?

3

One more rectanglular-shaped peice of metal siding needs to be cut to cover the exterior of a pole barn. The area of the piece is 30ft^2. The length is 1 less than 3 times the width. How wide should the metal piece be? Round to the nearest hundredth of a foot.

3.33 ft

If an object is dropped from a height of 200 feet, the function h(t)=-16t^2+200 gives the height of the object after 't' seconds. Approximately, when will the object hit the ground?

3.54 seconds

What is the value of 'n' so that the expression x^2+11x+n is a perfect square trinomial?

30.25

You are knitting a blanket. You want the area of the blanket to be 24 ft^2. You want the length of the blanket to be 2 ft longer than its width. What should the dimensions of the blanket be?

4 ft by 6 ft

A ball is thrown into the air with initial upward velocity of 60 ft/s. Its height (h) in feet after t seconds is given by the function h=-16t^2+60t+6. What will the height be at t=3 seconds?

42 feet

Water is added to two containers for 15 minutes. The equations below model the ounces of water, 'y', in each container after 'x' minutes. At the time when the containers hold the same amound of water, how much water do they hold? Container A: y=46x+120 Container B: y=-2x^2+60x+180

580 ounces

A box shaped like a rectangular prism has a height of 17 in and a volume of 2,720 in^3. The length is 4 inches greater than twice the width. What is the width of the box?

8 in

What is the solution of n^2-49=0?

=7

What is the solution of x^2+64=0?

=8

Graph the quadratic functions y=-2x^2 and y=-2x^2+4 on a seperate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs.

Both of the graphs have the same shape, however, the y=2x^2+4 has an upward translation of 4 on its graph. Therefore the position of the second graph is shifted upward by 4.

What values of a, b, and c would you use in the quadratic formula for the following question? 5x^3+9x=4

a=5, b=9, c=-4

Solve each equation by finding square roots. If the equation has no real-numbers solution, write 'no solution.'

b=+1/2

Solve by factoring. c^2=5c

c=0 or 5

What function can be used to model data pairs that have a common ratio?

exponential

What is the order, from narrowest to widest graph, of the quadratic functions f(x)=-10x^2, f(x)=2x^2,f(x)=0.5x^2

f(x)=-10x^2,f(x)=2x^2,f(x)=0,5^2

Solve each equation by finding square roots. If the equation has no real-number solution, write 'no solution.' 4g^2=25

g=+5/2

Solve by factoring. g^2+4g-32=0

g=4 or -8

How is the graph of y=-6x^2-4 different from the graph of y=-6x^2?

it is shifted 4 units down

Use the Zero Product Property to solve the equation. (4k+5)(k+7)=0

k=-5/4 or -7

Which kind of function best models the set of data points (-1,22), (0,6), (1,-10), (2,-26), and (3, -42)?

linear

Solve each equation by graphing the related function. If the equation has no real-numbers solution, write 'no solution.' x^2+7=0

no solution

Tell how many solutions the equation has. h^2=-49

no solution

What are the approximate solutions of 2x^2-x+10=0?

no solution

Which of the following is a solution of x^2+11x+112=0? If necessary, round to the nearest hundreth.

no solution

Which kind of function best models the set of data points (-3, 18), (-2, 6), (-1, 2), (0,11), and (1, 27)?

none of the above

How many real-number solutions does the equation have? 0=2x^2-20x+50

one solution

Tell how many solutions the equation has. S^2-35=-35

one solution

Solve each equation by finding square roots. If the equation has no real-number solution, write 'no solution.' 144-p^2=0

p=+12

Solve by factoring. p^2-4p=21

p=-3 or 7

Write the equation in standard form. Then solve. 4q^2+3q^2-4q+18

q=-9 or 2

Which method is the best method for solving the equation 8x^2-13x+3=0?

quadratic formula

A catapult launches a boulder with an upward velocity of 122 feet per second. The height of the boulder, (h), in feet after 't' seconds is given by the function h(t)=-16t^2+122t+10. How long does it take the boulder to reach its maximum height? What is the boulder's maximum height? Round to the nearest hundredth? What is the boulder's maximum height? Round to the nearest hundredth, if necessary.

reaches a maximum height of 242.56 feet after 3.81 seconds

Solve by factoring. s^2-14s+45=0

s=5 or 9

How many real number solutions does the equation have? 0=-4x^2+7x+8

two solution

Solve by factoring. 2w^2-11w=-12

w=3/2 or 4

Solve each equation by graphing the related function. If the equation has no real-number solution, choose 'no solution.' 1/4x^2-4=0

x=+4

What is the solution of x^2+6x=-5?

x=-1

Solve the equation using the quadratic formula. 4x^2+3x-10=0

x=-2, x=1.25

Solve the equation using the quadratic formula. -x^2+27=6x

x=-9, x=3

Solve each equation by graphing the related functions. If the equation has no real-number solution, write 'no solution.' 3x^2=0

x=0

Which equation represents the axis of symmetry of the function y=-2x^2+4x-6?

x=1

What are the solution of the equation? 0=x^2-2x-24

x=6,-4

Use the Zero Product Property to solve the equation. (x-9)(x-8)=0

x=8 or 9

Solve each equation by graphing the related function. If the equation has no real-number solution, write 'no solution.'

x^2-9=0

Which of the following functions has a rate of change that stays the same? - y=1/3x^2 - y=2^x - y=-7x+9 - y=x^2+1

y=-7x+9

Which of the following has a graph that is wider than the graph of y=3x^2+2?

y=0.5x^2+1

Which of the following functions has a rate of change that stays the same?

y=19x-10

Solve each equation by finding square roots. If the equation has no real-number solution, write 'no solution.' 5z^2-45=0

z=+3

Solve by factoring. 2z^2-21z-36=0

z=-3/2 or 12