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VashaNatasha [74]
4 years ago
13

Explain whether or not the following equation is a quadratic function in vertex form. y = 4(x - 2)^2 + 6.

Mathematics
1 answer:
steposvetlana [31]4 years ago
6 0

Answer:

Yes, the following equation is a quadratic function in vertex form

Step-by-step explanation:

we know that

The <u>quadratic function</u> of the vertical parabola into <u>vertex form</u> is equal to

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

where

(h,k) is the vertex of the parabola

If the <u>coefficient</u> a is > 0 ----> the parabola open upward (vertex is a minimum)

If the coefficient a is < 0 ----> the parabola open downward (vertex is a maximum)

in this problem we have

y=4(x-2)^{2} +6

The <u>squared term</u> contain the x-coordinate of the vertex

h=2

The <u>constant term</u> is the y-coordinate of the vertex

k=6

The vertex is the point (2,6)

The coefficient is equal to

a=4 ----> open upward (vertex is a minimum)

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2.) Use the Slope Intercept Form of a line to find the equation of the line from point C to point D.
mezya [45]

First we need slope

  • C=(0,0)
  • D(7,12)

\\ \sf\longmapsto m=\dfrac{12-0}{7-0}

\\ \sf\longmapsto m=\dfrac{12}{7}

Put D co-ordinates on y=mx+b

\\ \sf\longmapsto 12=\dfrac{12}{7}(7)+b

\\ \sf\longmapsto 12=12+b

\\ \sf\longmapsto b=12-12

\\ \sf\longmapsto b=0

Now

slope intercept form.

\\ \sf\longmapsto y=\dfrac{12}{7}x

  • As b=0
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2 years ago
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Find the LCD. 2/5, 1/2, and 3/4
harina [27]

Answer:

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Step-by-step explanation:

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3 years ago
Write the equation y=-1/2x+3 in standard form. how do I do this?
Lapatulllka [165]
Standard form is ax + by = c.  Begin our transformation by multiplying both sides by 2 to get rid of the fraction.  Notice that ax + by = c does not allow for fractions.  Doing that multiplication gives us 2y=-x + 3.  Now move the x over by the y by addition.  x + 2y = 3.  And there you go!
7 0
4 years ago
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What are the coordinates of the point on the directedline segment from K(-5,-4) to L(5,1) that partitionsthe segment into a rati
Diano4ka-milaya [45]
You can solve this either just plain algebra or with the use of trigonometry.
In this case, we'll just use algebra.
 
So, if we let M be the the point that partitions the segment into a ratio of 3:2, we have this relation:
KM/ML = 3/2
KM = 1.5 ML

We also have this:
KL = KM + ML
Substituting KM,
KL = (3/2) ML + ML
KL = 2.5 ML

Using the distance formula and the given coordinates of the K and L, we get the length of KL
KL = sqrt ( (5-(-5)^2 + (1-(-4))^2 ) = 5 sqrt(5)

Since,
KL = 2.5 ML

Substituting KL,
ML = (1/2.5) KL = (1/2.5) 5 sqrt(5) = 2 sqrt(5)

Using again the distance formula from M to L and letting (x,y) as the coordinates of the point M
ML = 2 sqrt(5) = sqrt ( (5-x)^2 + (1-y)^2 )   [let this be equation 1]

In order to solve this, we need to find an expression of y in terms of x. We can use the equation of the line KL.
The slope m is:
m = (1-(-4))/(5-(-5) = 0.5

Using the general form of the linear equation:
y = mx +b
We substitue m and the coordinate of K or L. We'll just use K.
-5 = (0.5)(-4) + b
b = -1.5

So equation of the line is
y = 0.5x - 1.5      [let this be equation 2]

Substitute equation 2 to equation 1 and solving for x, we get 2 values of x,
x=1, x=9

Since 9 does not make sense (it does not lie on the line), we choose x=1.
Using the equation of the line, we get y which is -1.

So, we get the coordinates of point M which is (1,-1)
3 0
3 years ago
Calculate the average rate of change for the given graph from x = 0 to x = 3 and select the correct answer below. (0,6) (3,0) ​
algol13

Answer:

(3,0)

Step-by-step explanation:

The number on the x axis is the only number that changes not the number on the y axis.  

5 0
4 years ago
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