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Leviafan [203]
3 years ago
13

Match the parabolas represented by the equations with their vertices. y = x2 + 6x + 8 y = 2x2 + 16x + 28 y = -x2 + 5x + 14 y = -

x2 + 7x + 7 y = 2x2 + 7x + 5 y = -2x2 + 8x + 5 Vertex Equation of Parabola (-1.75, -1.125) arrowRight (-3, -1) arrowRight (-4, -4) arrowRight (2.5, 20.25) arrowRight
Mathematics
1 answer:
GaryK [48]3 years ago
3 0

Consider all parabolas:

1.

y = x^2 + 6x + 8,\\y=x^2+6x+9-9+8,\\y=(x^2+6x+9)-1,\\y=(x+3)^2-1.

When x=-3, y=-1, then the point (-3,-1) is vertex of this first parabola.

2.

y = 2x^2 + 16x + 28=2(x^2+8x+14),\\y=2(x^2+8x+16-16+14),\\y=2((x^2+8x+16)-16+14),\\y=2((x+4)^2-2)=2(x+4)^2-4.

When x=-4, y=-4, then the point (-4,-4) is vertex of this second parabola.

3.

y =-x^2 + 5x + 14=-(x^2-5x-14),\\y=-(x^2-5x+\dfrac{25}{4}-\dfrac{25}{4}-14),\\y=-((x^2-5x+\dfrac{25}{4})-\dfrac{25}{4}-14),\\y=-((x-\dfrac{5}{2})^2-\dfrac{81}{4})=-(x-\dfrac{5}{2})^2+\dfrac{81}{4}.

When x=2.5, y=20.25, then the point (2.5,20.25) is vertex of this third parabola.

4.

y =-x^2 + 7x + 7=-(x^2-7x-7),\\y=-(x^2-7x+\dfrac{49}{4}-\dfrac{49}{4}-7),\\y=-((x^2-7x+\dfrac{49}{4})-\dfrac{49}{4}-7),\\y=-((x-\dfrac{7}{2})^2-\dfrac{77}{4})=-(x-\dfrac{7}{2})^2+\dfrac{77}{4}.

When x=3.5, y=19.25, then the point (3.5,19.25) is vertex of this fourth parabola.

5.

y =2x^2 + 7x +5=2(x^2+\dfrac{7}{2}x+\dfrac{5}{2}),\\y=2(x^2+\dfrac{7}{2}x+\dfrac{49}{16}-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x^2+\dfrac{7}{2}x+\dfrac{49}{16})-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x+\dfrac{7}{4})^2-\dfrac{9}{16})=2(x+\dfrac{7}{4})^2-\dfrac{9}{8}.

When x=-1.75, y=-1.125, then the point (-1.75,-1.125) is vertex of this fifth parabola.

6.

y =-2x^2 + 8x +5=-2(x^2-4x-\dfrac{5}{2}),\\y=-2(x^2-4x+4-4-\dfrac{5}{2}),\\y=-2((x^2-4x+4)-4-\dfrac{5}{2}),\\y=-2((x-2)^2-\dfrac{13}{2})=-2(x-2)^2+13.

When x=2, y=13, then the point (2,13) is vertex of this sixth parabola.

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24g

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According to​ statistics, a person will devote 34 years to sleeping and watching TV. The number of years sleeping will exceed th
Kobotan [32]

Considering the definition of an equation and the way to solve it, a person will devote 28 years watching TV and 6 years sleeping.

<h3 /><h3>Definition of equation</h3>

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

  • When a value that is adding, when passing to the other member of the equation, it will subtract.
  • If a value you are subtracting goes to the other side of the equation by adding.
  • When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.
  • If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.

<h3>This case</h3>

Being "x" the number of years watching TV, and knowing that:

  • The number of years sleeping will exceed the number of years watching TV by 22.
  • A person will devote 34 years to sleeping and watching TV.

the equation in this case is:

x + (x+22) =34

Solving:

x + x =34 -22

2x= 12

x= 12 ÷ 2

<u><em>x=6</em></u>

As the number of years sleeping will exceed the number of years watching TV by 22, then<u><em> x +22= 6 +22= 28 years.</em></u>

Finally, a person will devote 28 years watching TV and 6 years sleeping.

Learn more about equations:

brainly.com/question/4983716

brainly.com/question/13314678

#SPJ1

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2 years ago
The graph of f(x) = x2 + x - 6 is shown below.
guapka [62]

Answer:

the solutions of a function are the points where for some value of x the function becomes zero

thus the solns for this graph would be

<h3>-3 , 2</h3>

that's option 1.

3 0
2 years ago
The sum of the square of a positive number and the square of 44 more than the number is 8080. what is the​ number?
mash [69]
Let the number be x, therefore, its square is x², and 44 more than the number is x+44 whose square is (x+4)².
Thus the sum will be x² + (x+44)²² = 8080
                                  x² + x² + 88x + 1936= 8080 Combining the right terms 
                                  2x² + 8x - 6144 = 0 dividing by 2
                                     x² + 44x - 3072 =0 solving for x
                          x = 37.6 or -81.6
Therefore, the positive number is 37.6
                                
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a quarter before 6 = 5.45
So he needs to leave 23 mins before 5.45

23 mins before 5.45 = 5.22
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