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vfiekz [6]
3 years ago
7

Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?

Mathematics
2 answers:
slava [35]3 years ago
8 0

we have

y = -6x^{2} + 3x + 2

we know that

the vertex form of the vertical parabola equation is equal to

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

where

(h,k) is the vertex of the parabola

To find the equation rewritten in vertex form let's factor the equation

<u>Factor the leading coefficient </u>

y = -6(x^{2} - 0.5x) + 2

<u>Complete the square. Remember to balance the equation by adding the same constants to each side</u>

y = -6(x^{2} - 0.5x+0.0625-0.0625) + 2

y = -6(x^{2} - 0.5x+0.0625) + 2 +0.375

y = -6(x^{2} - 0.5x+0.0625) + 2.375

<u>Rewrite as perfect squares</u>

y = -6(x-0.25)^{2} + 2.375

therefore

the answer is

y = -6(x-0.25)^{2} + 2.375

Annette [7]3 years ago
4 0
The answer is y = -6( x- \frac{1}{4}) ^{2}+3

Regular form: y = ax² + bx + c
Vertex form: y = a(x - h)² + k
(h, k) - vertex

y = -6 x^{2} +3x+2 \\ y -2=-6 x^{2} +3x \\  y-2+6*=-6* x^{2} +6* \frac{1}{2} x \\  \\ y-2-6* \frac{1}{16} =-6* x^{2} +6* \frac{1}{2} x -6* \frac{1}{16} \\  \\ &#10;y -2 -\frac{6}{16} =-6( x^{2} -\frac{1}{2} x+\frac{1}{16}) \\  \\ &#10;y- \frac{2*16}{16} -\frac{6}{16} =-6( x^{2} -\frac{1}{2} x+(\frac{1}{4})^{2} ) \\  \\ &#10;y -  \frac{32}{16} -\frac{6}{16}  = -6( x- \frac{1}{4}) ^{2}  \\  \\ &#10;y -  \frac{32+6}{16} = -6( x- \frac{1}{4}) ^{2} \\  \\ &#10;y -  \frac{48}{16} =  -6( x- \frac{1}{4}) ^{2} \\  \\

y -  3=  -6( x- \frac{1}{4}) ^{2} \\  \\ &#10;y  =  -6( x- \frac{1}{4}) ^{2}+3&#10;

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Urgent!!! Will give thanks and branliest!
agasfer [191]
Okay so, togo flies 30 miles in 3/5 of an hour with the wind.togo flies 30 miles in 5/6 of an hour against the wind. his rate of speed with the wind was 30 / (3/5) = 30*5/3 = 150/3 = 50 mph.his rate of speed against the wind was 30 / (5/6) = 30*6/5 = 6*6 = 36 mph.3/5 of an hour times 50 mph = 30 miles.
5/6 of an hour times 36 mph = 30 miles.mph looks good.
going he was with the wind.
his rate of speed then was the airplane speed plus the wind speed.coming back he was against the wind.his rate of speed then was the airplane speed minus the wind speed.-----50 mph = A + W36 mph = A - W-----looks like A + W - (A - W) should equal 50 - 36.removing parentheses, equation becomesA + W - A + W = 14.
combining like terms, the equation becomes2*W = 14.dividing both sides by 2, equation becomesW = 7.if W = 7, then A can be found as follows:50 = A + 7A = 43.likewise,36 = A - 7A = 43.since the airplane speed is the same, it looks like the answer is good.solving in the original equations, we get3/5 * (43 + 7) = 303/5 * 50- = 3030 = 30good.-----5/6 * (43 - 7) = 305/6 * 36 = 3030 = 30good.
answer is W = 7 and A = 43.
8 0
3 years ago
Which equation is a radical equation.
OlgaM077 [116]

Hi there! :)


A radical equation is an equation in which a variable (ex. x, y, a, v) is under a radical sign. The only equation that has a variable under a radical (x) is the second option. There is an x next to the 2 under the radical.


I hope this helps, DM me if you have anymore questions. :)


~kaikers

6 0
3 years ago
Read 2 more answers
Scary math stuff hmmm
kirza4 [7]

Answer:

Deez

Step-by-step explanation:ok so you start with deez and then multiply that by the coefficient and got get nuts

8 0
3 years ago
Find the distance and midpoint of a segment with the following endpoints: (5,-1) and (-9,-1)
Likurg_2 [28]

Answer:

d = 14

(-2,-1)

General Formulas and Concepts:

  • Order of Operations: BPEMDAS
  • Distance Formula: d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
  • Midpoint Formula: (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Step-by-step explanation:

<u>Step 1: Define</u>

(5, -1)

(-9, -1)

<u>Step 2: Find distance </u><em><u>d</u></em>

  1. Substitute:                    d = \sqrt{(-9-5)^2+(-1-(-1))^2}
  2. Simplify:                        d = \sqrt{(-9-5)^2+(-1+1)^2}
  3. Subtract/Add:               d = \sqrt{(-14)^2+(0)^2}
  4. Evaluate:                       d = \sqrt{196}
  5. Evaluate:                       d = \14

<u>Step 3: Find Midpoint</u>

  1. Substitute:                    (\frac{5-9}{2},\frac{-1-1}{2})
  2. Subtract:                       (\frac{-4}{2},\frac{-2}{2})
  3. Divide:                          (-2,-1)
7 0
3 years ago
An image formed by a circular spotlight has a radius of 124 centimeters. What is the area of the circular image? Use 3.14 for pi
Lemur [1.5K]

area = pi X radius squared

 so area = 3.14 x 124^2

= 3.14 x 15376 = 48,280.64 square centimeters.

5 0
3 years ago
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