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Semenov [28]
3 years ago
12

If a quadratic equation is given to you in vertex form, what is the vertex?

Mathematics
2 answers:
fomenos3 years ago
8 0

Answer:

(-h,k)

Step-by-step explanation:

vertex form:

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

switch sign of h and you get the x

keep sign of k and you get y

ex- 3(x-5)+7

vertex=(5,7)

ziro4ka [17]3 years ago
4 0

If for example, you were given y = 2(x-3)^2 + 5, then the vertex is (3,5)

As another example, the equation y = 7(x+1)^2 + 10 has the vertex (-1,10)

The general vertex form is y = a(x-h)^2 + k with the vertex (h,k)

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Two boats started to move towards each other from two docks, located 30 miles apart. One boat moved at a speed of 2.5 miles per
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Step-by-step explanation:

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3 years ago
Y=-1/3x^2-4x-5 in vertex form
grigory [225]

Answer:

Y=-\frac{1}{3}(x+6)^2+7   [Vertex form]

Step-by-step explanation:

Given function:

Y=-\frac{1}{3}x^2-4x-5

We need to find the vertex form which is.,

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

where (h,k) represents the co-ordinates of vertex.

We apply completing square method to do so.

We have  

Y=-\frac{1}{3}x^2-4x-5

First of all we make sure that the leading co-efficient is =1.

In order to make the leading co-efficient is =1, we multiply each term with -3.

-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5

-3Y=x^2+12x+15

Isolating x^2 and x terms on one side.

Subtracting both sides by 15.

-3Y-15=x^2+12x-15-15

-3Y-15=x^2+12x

In order to make the right side a perfect square trinomial, we will take half of the co-efficient of x term, square it and add it both sides side.  

square of half of the co-efficient of x term = (\frac{1}{2}\times 12)^2=(6)^2=36

Adding 36 to both sides.

-3Y-15+36=x^2+12x+36

-3Y+21=x^2+12x+36

Since x^2+12x+36 is a perfect square of (x+6), so, we can write as:

-3Y+21=(x+6)^2

Subtracting 21 to both sides:

-3Y+21-21=(x+6)^2-21

-3Y=(x+6)^2-21

Dividing both sides by -3.

\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}

Y=-\frac{1}{3}(x+6)^2+7   [Vertex form]

8 0
3 years ago
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