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ololo11 [35]
3 years ago
9

What equation represents y=2x^2+24x+85 in vertex form

Mathematics
1 answer:
Andrej [43]3 years ago
8 0
Y=a(x-h)^2+k

vertex form is basically completing the square

what you do is
for
y=ax^2+bx+c
1. isolate x terms
y=(ax^2+bx)+c
undistribute a
y=a(x^2+(b/a)x)+c
complete the square by take 1/2 of b/a and squaring it then adding negative and postive inside
y=a(x^2+(b/a)x+(b^2)/(4a^2)-(b^2)/(4a^2))+c
complete square
too messy \
anyway

y=2x^2+24x+85
isolate
y=(2x^2+24x)+85
undistribute
y=2(x^2+12x)+85
1/2 of 12 is 6, 6^2=36
add neagtive and postivie isnde
y=2(x^2+12x+36-36)+85
complete perfect square
y=2((x+6)^2-36)+85
distribute
y=2(x+6)^2-72+85
y=2(x+6)^2+13

vertex form is
y=2(x+6)^2+13
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Answer:

132/100, or 1.32

Step-by-step explanation:

Just change 13/10 to 130/100 and add 2/100 to make it 132/100, or 1.32 :)

4 0
3 years ago
Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 450 newtons stretches a sprin
vlada-n [284]

Answer:

The work done is 202.50Nm

Step-by-step explanation:

Given

F =450N

x_1 = 30cm

x_2 = 60cm

Required

The work done

First, we calculate the spring constant (k)

F = kx_1

450N = k *30cm

k = \frac{450N}{30cm}

k =15N/cm

So:

F = kx_1

F(x) = 15x

The work done using Hooke's law is:

W =\int\limits^a_b {F(x)} \, dx

This gives:

W =\int\limits^{60}_{30} {15x} \, dx

Rewrite as:

W =15\int\limits^{60}_{30} {x} \, dx

Integrate

W =15 \frac{x^2}{2}|\limits^{60}_{30}

This gives:

W =15 *\frac{60^2 - 30^2}{2}

W =15 *\frac{2700}{2}

W =15 *1350

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Convert to Nm

W =\frac{20250Nm}{100}

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3 years ago
What is the same as 15.39÷100
marysya [2.9K]

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NEED HELP URGENT!! How do I solve this on number 30?(please go through the steps)
tatiyna

x^2+6x-5=0

x^2=2x

2x+6x-5=0

2x+6x=8x

8x-5=0

+5 +5

(if you don’t know what I’m doing here is that I’m removing the negative 5 by putting a positive 5 since both of them make 0. Also the “x” always stay alone and the unit stays as the unit)

(I putted the positive under the 0 because what u do to the unit you need to do the same thing with the other.)

8x/8=5/8

(If ur lost here it means dividing.)

The answer

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