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svet-max [94.6K]
3 years ago
11

I need another graphing quadratic pointer f(x)=x square -18x +80

Mathematics
1 answer:
swat323 years ago
4 0
F(x)=x^2-18x+80
ok so remember
you need to know
1. degree of function- tells what kind of graph
2. leading term- tells which direction graph opens
3. xintercept and y intercepts
4. vertex

ok so in form
f(x)=ax^2+bx+c 

1.
degree, 2nd degree so parabola

2.
a=leading terma=+1 in this case so the graph opens up and is a normal graph

3.xintercept is where graph crosses x axis or where y=0, y=f(x) so
0=x^2-18x+80
0=(x-8)(x-10)
xints are (8,0) and (10,0)
y intercept is where cross y axis or where x=0
set x=0
yint=0^2-18(0)+80
yint=80
yint=(0,80)

4. vertex (vertex is highest point if graph opens down, and lowest point if graph opens up)
if in form f(x)=ax^2+bx+c, the x value of the vertex is given by -b/(2a) so
b=-18
a=1
-(-18)/2(1)
18/2=9
input
9^2-18(9)+80=yvalue
-1=yvalue
vertex=(9,-1)

so we have
1. graph is parabola
2. opens up
3. crosses through points (8,0), (10,0), (0,80)
4. vertex=(9,-1)

so we plot the points (8,0), (10,0), (0,80) and (9,-1)  and draw a prabola opening up with (9,-1) as the highest point
attachment below ( it might be hard to graph (0,80) since it is so high up so you don't have to graph that point)


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lara [203]

It will take exactly 4 years for these trees to be the same height

Step-by-step explanation:

A gardener is planting two types of trees:

  • Type A is 3 feet tall and grows at a rate of 7 inches per year
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We need to find in how many years it will take for these trees to be the

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Assume that it will take x years for these trees to be the same height

The height of a tree = initial height + rate of grow × number of years

Type A:

∵ The initial height = 3 feet

∵ 1 foot = 12 inches

∴ The initial height = 3 × 12 = 36 inches

∵ The rate of grows = 7 inches per year

∵ The number of year = x

∴ h_{A} = 36 + (7) x

∴ h_{A} = 36 + 7 x

Type B:

∵ The initial height = 5 feet

∴ The initial height = 5 × 12 = 60 inches

∵ The rate of grows = 1 inches per year

∵ The number of year = x

∴ h_{B} = 60 + (1) x

∴ h_{B} = 60 + x

Equate h_{A} and h_{B}

∴ 36 + 7 x = 60 + x

- Subtract x from both sides

∴ 36 + 6 x = 60

- Subtract 36 from both sides

∴ 6 x = 24

- Divide both sides by 6

∴ x = 4

∴ The two trees will be in the same height in 4 years

It will take exactly 4 years for these trees to be the same height

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You can learn more about the rate in brainly.com/question/10712420

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If x = 8 units, y = 3 units, and h = 10 units, find the area of the trapezoid shown above using decomposition.
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Using long division to find the quotient, what changes do you first
lora16 [44]

Answer:

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Step-by-step explanation:

Given

Dividend = 125x^3 - 8

Divisor = 5x - 2

Required

Determine the quotient

See attachment for complete process.

First, divide 125x^3 by 5x

\frac{125x^3}{5x} =25x^2

Write 25x^2 at the top

Multiply 5x - 2 by 25x^2

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Subtract from 125x^3 - 8

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125x^3 - 8 - (125x^3 - 50x^2) = 50x^2 - 8

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Divide 50x^2 by 5x

\frac{50x^2}{5x} = 10x

Write 10x at the top

Multiply 5x - 2 by 10x

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Subtract from 50x^2 - 8

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50x^2 - 8 - (50x^2 - 20x) = 20x - 8

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Divide 20x by 5x

\frac{20x}{5x} = 4

Write 4 at the top

Multiply 5x - 2 by 4

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Subtract from 20x - 8

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20x - 8 - (20x - 8) = 0

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