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dem82 [27]
3 years ago
10

Y=-3x^2-6x+24

Mathematics
1 answer:
Lera25 [3.4K]3 years ago
3 0
The x-intercept is the point at which the function intersects the x-axis.
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.

y=-3x^2-6x+24 \\ 0=-3x^2-6x+24

Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.

0=-3x^2-12x+6x+24\\0=-3x(x+4)+6(x+4)\\0=(-3x+6)(x+4)

Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.

-3x+6 = 0
-3x = -6
x = 2

x+4 = 0
x = -4

Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.

Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.

y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24

What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.

y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27

Thus the vertex is (-1, 27)

The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)

As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)




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the Children's Hospital sponsors a 10k race to raise money. it receives $75 per race entry and $10,000 in donations but it must
masha68 [24]

Answer:

There would need to be at least 1,800 entries in order for them to meet their goal.

Step-by-step explanation:

To find this, we must write an equation that helps solve it. We know that for every entry (x), we gain 75 and lose 25. We can express this as the following.

75x - 25x

Then we can add the number of donations.

75x - 25x + 10,000

Then we can set it as greater than or equal to the goal number.

75x - 25x + 10,000 ≥ 100,000

Now we solve this using the order of operations.

75x - 25x + 10,000 ≥ 100,000 ----> Combine like terms

50x + 10,000 ≥ 100,000 ------> Subtract 10,000

50x ≥ 90,000 -----> Divide by 50

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4 0
3 years ago
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farouk scored 110% in his last mathematics test.Explain how this is possible.Give an actual mark allocations that will prove you
irakobra [83]

Answer:

Grades higher than 100% can be achieved by doing extra credit and/or answering bonus questions.

hope this helps! :)

8 0
2 years ago
A company makes three sizes of juice bottles: small, medium, and large.
Ivahew [28]

An expression in terms of s that represents the number of large bottles is :  L = (\frac{15s}{2} /3})

<h3>Ratio of different sizes of bottles </h3>

The company makes s small bottles every minute

let ; M represent the number of medium bottles made every minute

L represent the number of large bottles made every minute

small bottles to medium =  2 : 3

small bottles to medium =  s : M

M is the unknown, so to find how many medium bottles that has been made,  we must cross multiply

2M = 3s

M = \frac{3s}{2}  medium bottles made every minute

medium bottles to large bottles =  3 : 5

medium bottles to large bottles =  M : L

where M = \frac{3s}{2}

The equation becomes:

           3 : 5

           \frac{3s}{2} : L

L is the unknown, so to find how many Large bottles that has been made,  we must cross multiply

3L =( \frac{3s}{2} ) * 5

L = (\frac{15s}{2} /3})

L = ( \frac{5}{2} s)

L = 2.5 s

therefore the large bottles the company makes every minute is 2.5s large bottles

we can conclude that the expression for the number of large bottles the company makes every minute with respect to s is : L = 2.5 s

Learn more about Ratio : brainly.com/question/1509142

8 0
1 year ago
A circle with circumference 20 has an arc with 72 degree central angle what is length of the arc
Debora [2.8K]

Answer:

<h2>4</h2>

Step-by-step explanation:

<em>Look at the picture.</em>

<em />

<em>At the beginning we have to calculate what part of the angle 360° is the given angle 75°.</em>

<em />\dfrac{75}{360}=75:360=0.2<em />

<em>The same part of the circumference of the circle is the arc defined by this central angle.</em>

The circumference <em>C = 20</em>.

Therefore

x=0.2\cdot20=4

4 0
2 years ago
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Tcecarenko [31]

Answer:

0.5 seconds

Step-by-step explanation:

On the ground, height is 0

-16t² + 4 = 0

16t² = 4

t² = 4/16

t² = ¼

t = ½

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3 years ago
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