Which equation is in point-slope form and is depicted by the line in this graph?

Put the quadratic into vertex form and state the coordinates of the vertex. y= y= \,\,x^2-6x-3 x 2 −6x−3

enot [183]

Answer:

$y = (x - 3)^2 - 12$

$(3,-12)$

Step-by-step explanation:

Given

$y = x^2 - 6x - 3$

Solving (a): In vertex form

The vertex form of an equation is:

$y = a(x - h)^2 + k$

To do this, we make use of completing the square method.

We have:

$y = x^2 - 6x - 3$

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Take the coefficient of x (i.e. -6)

Divide by 2; -6/2 = -3

Square it: (-3)^2 = 9

Add and subtract the result to the equation

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$y = x^2 - 6x - 3$

$y = x^2 - 6x + 9 - 9 - 3$

$y = x^2 - 6x + 9 - 12$

Factorize $x^2 - 6x + 9$

$y = x^2 - 3x-3x + 9 - 12$

$y = x(x - 3)-3(x - 3) - 12$

Factor out x - 3

$y = (x - 3)(x - 3) - 12$

Express as squares

$y = (x - 3)^2 - 12$

Hence, the vertex form of $y = x^2 - 6x - 3$ is: $y = (x - 3)^2 - 12$

Solving (b): State the coordinates of the vertex.

In $y = a(x - h)^2 + k$ ; the vertex is: (h,k)

The vertex of $y = (x - 3)^2 - 12$ will be $(3,-12)$

3 0

2 years ago

Quincy deposits $400 in a new bank account that earns 4 simple interest per year. What is the total amount in the account after

Kobotan [32]

Ÿū tj Yates tu hamase de Beas

6 0

3 years ago

I need answers pls now

Vesnalui [34]

Theres too many questions to answer dude, we aint gonna do your homework for you dude, give us one question N we'll help you solve and help you understand. school is all about understanding and not punishment

5 0

3 years ago

SOS if anyone could help that would be appreciated!!!❤️

Anastaziya [24]

Answer:

See below

Step-by-step explanation:

$2e)15-4x=10x+45$

Solve:

$15-4x=10x+45\\-4x-10x=45-15\\-14x=30\\ \boxed {x=-\dfrac{15}{7}}$ $3(x+1)=21$

Check:

$15-4 \left(-\dfrac{15}{7} \right)=10\left(-\dfrac{15}{7} \right)+45$

$15+\dfrac{60}{7} \right)=-\dfrac{150}{7} +45$

$\dfrac{210}{7} =30$

$30=30$

$3a) 3(x+1)=21$

Solve:

$3(x+1)=21\\3x+3=21\\3x=18\\x=6$

$3b) 2+3(x+1)=6x$

$2+3x+3=6x\\5=3x\\$

$x=\dfrac{5}{3}$

$3c) -2(2x-3)=-2$

Solve:

$-2(2x-3)=-2\\-4x+6=-2\\-4x=-8\\x=2$

3 0

3 years ago

Does anyone know the answer for the question below.

8090 [49]

Answer: option C

Step-by-step explanation:

The diagram of the triangle is shown in the attached photo. The triangle is a right angle triangle ABC

Assuming the given angle is #,

Recalling the trigonometric ratio,

tan # = opposite / adjacent

If tan # = 4, it means

opposite / adjacent = 4/1

Therefore, opposite = 4 and adjacent = 1

Applying Pythagoras theorem,

Hypotenuse^2 = opposite ^2 + adjacent ^2

Hypotenuse = AC

Opposite = 4

Adjacent = 1

AC^2 = 4^2 + 1^2 = 17

AC = ± √17

To determine cos #, we would apply another trigonometric ratio,

Cos# = adjacent /hypotenuse

Cos# = 1/±√17

Cos # =-1 /√17 or 1/√17

8 0

3 years ago