# 10.5 Graphing quadratic equations  (Page 7/15)

 Page 7 / 15

$y=5{x}^{2}+2$

$y=2{x}^{2}-4x+1$

$y\text{:}\phantom{\rule{0.2em}{0ex}}\left(0,1\right);x\text{:}\phantom{\rule{0.2em}{0ex}}\left(1.7,0\right),\left(0.3,0\right);$
axis: $x=1;\phantom{\rule{0.2em}{0ex}}\text{vertex}\text{:}\phantom{\rule{0.2em}{0ex}}\left(1,-1\right)$

$y=3{x}^{2}-6x-1$

$y=2{x}^{2}-4x+2$

$y\text{:}\phantom{\rule{0.2em}{0ex}}\left(0,2\right)\phantom{\rule{0.2em}{0ex}}x\text{:}\phantom{\rule{0.2em}{0ex}}\left(1,0\right);$
axis: $x=1;\phantom{\rule{0.2em}{0ex}}\text{vertex:}\phantom{\rule{0.2em}{0ex}}\left(1,0\right)$

$y=-4{x}^{2}-6x-2$

$y=\text{−}{x}^{2}-4x+2$

$y\text{:}\phantom{\rule{0.2em}{0ex}}\left(0,2\right)\phantom{\rule{0.2em}{0ex}}x\text{:}\phantom{\rule{0.2em}{0ex}}\left(-4.4,0\right),\left(0.4,0\right);$
axis: $x=-2;\phantom{\rule{0.2em}{0ex}}\text{vertex:}\phantom{\rule{0.2em}{0ex}}\left(-2,6\right)$

$y={x}^{2}+6x+8$

$y=5{x}^{2}-10x+8$

$y\text{:}\phantom{\rule{0.2em}{0ex}}\left(0,8\right);x\text{:}\phantom{\rule{0.2em}{0ex}}\text{none};$
axis: $x=1;\text{vertex}\text{:}\phantom{\rule{0.2em}{0ex}}\left(1,3\right)$

$y=-16{x}^{2}+24x-9$

$y=3{x}^{2}+18x+20$

$y\text{:}\phantom{\rule{0.2em}{0ex}}\left(0,20\right)\phantom{\rule{0.2em}{0ex}}x\text{:}\phantom{\rule{0.2em}{0ex}}\left(-4.5,0\right),\left(-1.5,0\right);$
axis: $x=-3;\phantom{\rule{0.2em}{0ex}}\text{vertex:}\phantom{\rule{0.2em}{0ex}}\left(-3,-7\right)$

$y=-2{x}^{2}+8x-10$

Solve Maximum and Minimum Applications

In the following exercises, find the maximum or minimum value.

$y=2{x}^{2}+x-1$

The minimum value is $-\frac{9}{8}$ when $x=-\frac{1}{4}$ .

$y=-4{x}^{2}+12x-5$

$y={x}^{2}-6x+15$

The minimum value is 6 when $x=3$ .

$y=\text{−}{x}^{2}+4x-5$

$y=-9{x}^{2}+16$

The maximum value is 16 when $x=0$ .

$y=4{x}^{2}-49$

In the following exercises, solve. Round answers to the nearest tenth.

An arrow is shot vertically upward from a platform 45 feet high at a rate of 168 ft/sec. Use the quadratic equation $h=-16{t}^{2}+168t+45$ to find how long it will take the arrow to reach its maximum height, and then find the maximum height.

In 5.3 sec the arrow will reach maximum height of 486 ft.

A stone is thrown vertically upward from a platform that is 20 feet high at a rate of 160 ft/sec. Use the quadratic equation $h=-16{t}^{2}+160t+20$ to find how long it will take the stone to reach its maximum height, and then find the maximum height.

A computer store owner estimates that by charging $x$ dollars each for a certain computer, he can sell $40-x$ computers each week. The quadratic equation $R=\text{−}{x}^{2}+40x$ is used to find the revenue, $R$ , received when the selling price of a computer is $x$ . Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.

20 computers will give the maximum of $400 in receipts. A retailer who sells backpacks estimates that, by selling them for $x$ dollars each, he will be able to sell $100-x$ backpacks a month. The quadratic equation $R=\text{−}{x}^{2}+100x$ is used to find the $R$ received when the selling price of a backpack is $x$ . Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue. A rancher is going to fence three sides of a corral next to a river. He needs to maximize the corral area using 240 feet of fencing. The quadratic equation $A=x\left(240-2x\right)$ gives the area of the corral, $A$ , for the length, $x$ , of the corral along the river. Find the length of the corral along the river that will give the maximum area, and then find the maximum area of the corral. The length of the side along the river of the corral is 120 feet and the maximum area is 7,200 sq ft. A veterinarian is enclosing a rectangular outdoor running area against his building for the dogs he cares for. He needs to maximize the area using 100 feet of fencing. The quadratic equation $A=x\left(100-2x\right)$ gives the area, $A$ , of the dog run for the length, $x$ , of the building that will border the dog run. Find the length of the building that should border the dog run to give the maximum area, and then find the maximum area of the dog run. ## Everyday math In the previous set of exercises, you worked with the quadratic equation $R=\text{−}{x}^{2}+40x$ that modeled the revenue received from selling computers at a price of $x$ dollars. You found the selling price that would give the maximum revenue and calculated the maximum revenue. Now you will look at more characteristics of this model. Graph the equation $R=\text{−}{x}^{2}+40x$ . Find the values of the x -intercepts. 1. $\left(0,0\right),\left(40,0\right)$ #### Questions & Answers where's the answers? Ed Reply I don't see where the answers are. Ed Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart? Maddy Reply 3 Christopher 18t+14t=96 32t=96 32/96 3 Christopher show that a^n-b^2n is divisible by a-b Florence Reply What does 3 times your weight right now Cherokee Reply Use algebra to combine 39×5 and the half sum of travel of 59+30 Cherokee What is the segment of 13? Explain Cherokee my weight is 49. So 3 times is 147 Cherokee kg to lbs you goin to convert 2.2 or one if the same unit your going to time your body weight by 3. example if my body weight is 210lb. what would be my weight if I was 3 times as much in kg. that's you do 210 x3 = 630lb. then 630 x 2.2= .... hope this helps tyler How to convert grams to pounds? paul What is the lcm of 340 Kendra Reply Yes Cherokee How many numbers each equal to y must be taken to make 15xy Malik Reply 15x Martin 15x Asamoah 15x Hugo 1y Tom 1y x 15y Tom find the equation whose roots are 1 and 2 Adda Reply (x - 2)(x -1)=0 so equation is x^2-x+2=0 Ranu I believe it's x^2-3x+2 NerdNamedGerg because the X's multiply by the -2 and the -1 and than combine like terms NerdNamedGerg find the equation whose roots are -1 and 4 Adda Ans = ×^2-3×+2 Gee find the equation whose roots are -2 and -1 Adda (×+1)(×-4) = x^2-3×-4 Gee Quadratic equations involving factorization Winner Reply there's a chatting option in the app wow Nana That's cool cool Nana Nice to meet you all Nana you too. Joan 😃 Nana Hey you all there are several Free Apps that can really help you to better solve type Equations. Debra Debra, which apps specifically. ..? Nana am having a course in elementary algebra ,any recommendations ? samuel Samuel Addai, me too at ucc elementary algebra as part of my core subjects in science Nana me too as part of my core subjects in R M E Ken at ABETIFI COLLEGE OF EDUCATION Ken ok great. Good to know. Joan 5x + 1/3= 2x + 1/2 sanam Plz solve this sanam 5x - 3x = 1/2 - 1/3 2x = 1/6 x = 1/12 Ranu Thks ranu sanam a trader gains 20 rupees loses 42 rupees and then gains ten rupees Express algebraically the result of his transactions vinaya Reply a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs$6.04 per gallon and the soda costs $4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs$5.71 per gallon?
Mohamed Reply
(a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r)
muhammad Reply
4x-7y=8 2x-7y=1 what is the answer?
Ramil Reply
x=7/2 & y=6/7
Pbp
x=7/2 & y=6/7 use Elimination
Debra
true
bismark
factoriz e
usman
4x-7y=8 X=7/4y+2 and 2x-7y=1 x=7/2y+1/2
Peggie
Ok cool answer peggie
Frank
thanks
Ramil
copy and complete the table. x. 5. 8. 12. then 9x-5. to the 2nd power+4. then 2xto the second power +3x
Sandra Reply
What is c+4=8
Penny Reply
2
Letha
4
Lolita
4
Rich
4
thinking
C+4=8 -4 -4 C =4
thinking
I need to study
Letha
4+4=8
William
During two years in college, a student earned $9,500. The second year, she earned$500 more than twice the amount she earned the first year.
Nicole Reply
9500=500+2x
Debra
9500-500=9000 9000÷2×=4500 X=4500
Debra
X + Y = 9500....... & Y = 500 + 2X so.... X + 500 + 2X = 9500, them X = 3000 & Y = 6500
Pbp

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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