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2 years ago

What is the vertex form of y=-1/2x^2 -2x -3?

Mathematics

1 answer:

STALIN [3.7K]2 years ago

4 0

Answer:

y = − 1 2 ⋅ ( x + 2 ) 2 − 1

Step-by-step explanation:

To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square. Let's see an example. Convert y = 2x2 - 4x + 5 into vertex form, and state the vertex. Equation in y = ax2 + bx + c form.

Very glad I could help you!1

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Please help me. I will give brainliest.

Ber [7]

Hey!

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Points:

(-2, 3) and (3, 0)

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Find the slope:

$= \frac{y2 - y1}{x2 - x1} \\=\frac{0 - 3}{3 - (-2)}\\= \frac{-3}{5} or -0.8$

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Slope Intercept Form:

y = mx + b

m = slope

b = y-intercept

Slope = -3/5

Y-intercept = 9/5

Answer: y = -3/5 + 9/5

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Point Slope Form:

y - y1 = m(x - x1)

You can use either of the points.

Answer:

y - 3 = -3/5(x - 2)

y - 0 = -3/5(x - 3)

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Hope This Helped! Good Luck!

3 0

3 years ago

Read 2 more answers

How many liters of 60% alcohol solution should be added to 40 liters of a 20% alcohol solution to make a 50% solution?

kolbaska11 [484]

Answer:

120 liters of 60% alcohol solution is needed

Step-by-step explanation:

Let's assume

x liters of 60% alcohol solution is added

so, we get solution as

$=\frac{60}{100}\times x$

$=0.6x$

we are given

40 liters of a 20% alcohol solution is

$=40\times\frac{20}{100}$

$=8$

so, total alcohol solution is

$=8+0.6x$

now, we can find total solutions

total solutions is

$=x+40$

now, it is making 50% solution

so, we get

$\frac{8+0.6x}{x+40} =\frac{50}{100}$

now, we can solve for x

$\left(8+0.6x\right)\cdot \:100=\left(x+40\right)\cdot \:50$

$800+60x=50x+2000$

$10x=1200$

$x=120$

So,

120 liters of 60% alcohol solution is needed

4 0

2 years ago

Write 82.25% as a fraction in simplest form

tiny-mole [99]

The Answer To your Question is: 33/40

8 0

2 years ago

On average, a commercial airplane burns about 3.9 × 10³ mL of gasoline per second. There can be as many as 5.1 × 10³ airplanes i

algol13

We use the given data above to calculate the volume of gasoline that is being burned per minute by commercial airplanes.

Amount burned of 1 commercial airplane = 3.9 × 10³ ml of gasoline per second
Number of airplanes = 5.1 × 10³ airplanes

We calculate as follows:

 3.9 × 10³ ml of gasoline per second / 1 airplane (5.1 × 10³ airplanes)(60 second / 1 min ) = 1.2 x 10^9 mL / min

8 0

3 years ago

Read 2 more answers

Use Newton's method to find an approximate solution of ln(x)=10-x. Start with x_0 =9 and find x_2 .

vova2212 [387]

Answer:

x₂ = 7.9156

Step-by-step explanation:

Given the function ln(x)=10-x with initial value x₀ = 9, we are to find the second approximation value x₂ using the Newton's method. According to Newtons method xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ)

If f(x) = ln(x)+x-10

f'(x) = 1/x + 1

f(9) = ln9+9-10

f(9) = ln9- 1

f(9) = 2.1972 - 1

f(9) = 1.1972

f'(9) = 1/9 + 1

f'(9) = 10/9

f'(9) = 1.1111

x₁ = x₀ - f(x₀)/f'(x₀)

x₁ = 9 - 1.1972/1.1111

x₁ = 9 - 1.0775

x₁ = 7.9225

x₂ = x₁ - f(x₁)/f'(x₁)

x₂ = 7.9225 - f(7.9225)/f'(7.9225)

f(7.9225) = ln7.9225 + 7.9225 -10

f(7.9225) = 2.0697 + 7.9225 -10

f(7.9225) = 0.0078

f'(7.9225) = 1/7.9225 + 1

f'(7.9225) = 0.1262+1

f'(7.9225) = 1.1262

x₂ = 7.9225 - 0.0078/1.1262

x₂ = 7.9225 - 0.006926

x₂ = 7.9156

Hence the approximate value of x₂ is 7.9156

7 0

2 years ago