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Katena32 [7]
3 years ago
11

Write an equation of the parabola in vertex form

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
4 0

Step-by-step explanation:

Recall that a parabola is the graph representing a quadratic equation, which is standard form is as follows:

y = ax2 + bx + c

where the value of 'a' determines whether the parabola opens upwards of downwards (i.e., the parabola opens upwards if a>0 and opens downwards if a<0) and the axis of symmetry is given by the line x = -b/(2a).

The vertex form of a parabola's (or a quadratic) equations is given by the following formula:

y = a(x - h)2 + k , where (h, k) is the vertex and the axis of symmetry is given by the line x = h.

Given that the vertex is at (0, 3), then ..... h = 0 and k = 3 ..... thus,

y = a(x - 0)2 + 3

y = a(x)2 + 3

With a point at (-4, -45), then ..... x = -4 and y = -45 ..... therefore,

-45 = a(-4)2 + 3

-45 = a(16) + 3

Solve for a by first subtracting 3 from both sides of the equation then dividing both sides of the equation by 16:

-45 - 3 = a(16) + 3 - 3

-48 = a(16)

-48/16 = 16a/16

-3 = a

With a vertex (h, k) at (0, 3) and given that a = -3, then the equation of this parabola in vertex form is as follows:

y = a(x - h)2 + k

y = -3(x - 0)2 + 3

y = -3x2 + 3

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8.Find the value of c that makes the expression be a perfect square trinomial p^2-30p+c
Darina [25.2K]
Hope this is the right one.

Problem 8
p^2 - 30p + c
<em>Step One</em>
Take 1/2 of - 30
1/2 * -30 = - 15

<em>Step 2
</em>Square -15
(-15)^2 = 225
c = 225

Problem Nine
\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} &#10;
a = 1
b = 4
c = -15
\text{x = }\dfrac{ -4 \pm \sqrt{4^{2} - 4*1*(-15) } }{2*1}
\text{x = }\dfrac{ -4 \pm \sqrt{\text{16} + \text{60} } }{2}

x = [-4 +/- sqrt(76)] / 2
x = [-4 +/- 2*sqrt19]/2
x = [-4/2 +/- 2/2 sqrt[19]
x = - 2 +/- sqrt(19) 

x1 = - 2 + sqrt(19)
x2 = -2 - sqrt(19)

These two can be broken down more by finding the square root. I will leave them the way they are.  It's just a calculator question if you want it to go into decimal form.

Problem Ten

a = 1
b = 4
c = -32

The discriminate is sqrt(b^2 - 4ac)
D = sqrt(b^2 - 4ac)
D = sqrt(4^2 - 4(1)(-32)
D = sqrt(16 - - 128)
D = sqrt(16 + 128)
D = sqrt(144)
D = +/- 12

Since D can equal + or minus 12 there must be 2 possible (and different) roots. As a matter of fact, this quadratic can be factored.
(x + 8)(x - 4) = y 
But that' s not what you were asked for.
The discriminate is >  0 so the roots are going to be real.
<em>Answer; The discriminate is > 0 so there will be 2 real different roots.</em>

4 0
2 years ago
Find the 7th term in the<br> sequence<br> -1, -3, -9,...
mestny [16]

Answer:

The answer is 729

Step-by-step explanation:

to get the next term, the sequence multiples the previous number by -3

1 * -3 = -3

-3 * -3 = 9

and so on.

To get the 7th term:

-27 * -3 = 81 (5th term)

81 * -3 = -243 (6th)

-243 * -3 = 729 (7th)

7 0
2 years ago
Read 2 more answers
Not really getting this can someone plz explain.
Komok [63]

your answer would be b becuase that is 3/6 so thats half and ou would simply it and 1/4 do the same

7 0
2 years ago
Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27\pi
anyanavicka [17]

Question:

Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27\pi27π27, pi cm^3 3 start superscript, 3, end superscript of melted purple liquid. The radius of the cone is 333 cm. What is the height of the cone?

Answer:

The height of the cone is 9 \ cm

Explanation:

It is given that the radius of the cone is 3 \ cm

The volume of the cone is 27\pi

The height of the cone can be determine using the formula,  

$V=\frac{1}{3} \pi r^{2} h$

Substituting the values V=27 \pi and r=3, we get,

$27 \pi=\frac{1}{3} \pi(3)^{2} h$

Multiplying both sides by 3, we have,

$81 \pi= 9\pi h$

Dividing both sides by $9 \pi$, we have,

9=h

Thus, the height of the cone is 9 \ cm

4 0
3 years ago
HELPP ITS A 60 min test and a alr took up most of my time watching t|k tok :} so now i have 20 mins left I will Give Brainlest!
soldi70 [24.7K]

Answer:

C

The "inverse operation" is just a way of saying "what do you do to isolate the variable". In this case, we isolate y, so we have to move all terms to the right side. To do that, we subtract 12 from each side to there will only be "y" on the left side.

8 0
2 years ago
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