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Anna [14]
3 years ago
7

Identify the vertex for the graph of y = 2x2 + 8x − 3. (2, 21) (2, 17) (−2, −11) (−2, −27)

Mathematics
2 answers:
Finger [1]3 years ago
5 0
\bf \textit{vertex of a vertical parabola, using coefficients}
\\\\
\begin{array}{lcccl}
y = & 2x^2& +8x& -3\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\qquad 
\left(-\cfrac{ b}{2 a}\quad ,\quad   c-\cfrac{ b^2}{4 a}\right)
\\\\\\
\left( -\cfrac{8}{2(2)}~~,~~-3-\cfrac{8^2}{4(2)} \right)\implies \left( \cfrac{-8}{4}~~,~~-3-\cfrac{64}{8} \right)
\\\\\\
\left(-2~~,~~-3-8  \right)\implies (-2~~,~~-11)
BlackZzzverrR [31]3 years ago
4 0

Answer:

The vertex is (-2, -11 ).

Step-by-step explanation:

Here, the given equation is,

y = 2x^2 + 8x - 3  -----(1)

Which is a parabola along x-axis,

Since, the standard form of parabola along x-axis is,

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

Where (h,k) is the vertex of the parabola,

By solving it,

y = ax^2 - 2ahx + ah^2 + k -----(2),

By comparing equation (1) and (2),

We get,

a = 2,   -2ah = 8 and ah² + k = - 3

⇒ -2(2) h = 8 ⇒ - 4 h = 8 ⇒ h = -2

And, (2)(-2)² + k = - 3

⇒ 8 + k = - 3

⇒ k = -11

Hence, the vertex of the given equation is (-2, -11 )

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THe product of three numbers is 3150. Two of the number are 14 and 15. Find the third number
Sholpan [36]

Answer:

15

Step-by-step explanation:

Let's call the mystery number x.

14\cdot 15\cdot x=3150 \\\\210x=3150 \\\\x=3150/210=15

Hope this helps!

4 0
3 years ago
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antiseptic1488 [7]
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5 0
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Represent the following expressions as a power of the number (a≠0):
Vsevolod [243]
The answer should be a^7
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3 years ago
I need a answer to this question please help
Burka [1]
  1. Since the triangles are similar, the slope of line segment AD and line segment BD are the same.
  2. The initial value and slope of the graph are 66 and 44 respectively.

<h3>Why are the two slopes the same?</h3>

Considering the two right-angled triangles (ΔABD and ΔBCE) with the following points A(2, 154), B(1, 110), D(2, 110) and E(1, 66).

Since the triangles are similar, the slope of line segment AD is given by:

Tanθ = AD/BE

Tanθ = (154 - 110)/(110 - 66)

Tanθ = 44/44

Tanθ = 1.

Also, the slopes of line segment BD is given by:

Tan∅ = BD/CE

Tan∅ = (2 - 1)/(1 - 0)

Tan∅ = 1/1

Tan∅ = 1.

Therefore, the slope of line segment AD and line segment BD are the same because θ is equal to ∅.

<h3>What are the initial value and slope of the graph?</h3>

By critically observing the graph, we can logically deduce that the initial value of this graph is 66 and it represents the shark's distance at the initial time (0 minute).

For the slope, we have:

Slope = Δy/Δx

Slope = (154 - 66)/(2 - 0)

Slope = 88/2

Slope = 44.

Read more on slope here: brainly.com/question/17601248

#SPJ1

<u>Complete Question:</u>

The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:

Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the same as the slope of the graph between points A and C.

Part B: What are the initial value and slope of the graph, and what do they represent?

6 0
2 years ago
A fishing hook is at an elevation of −12 m relative to sea level. Half an hour later, the fishing hook's elevation increases by
yulyashka [42]

Answer:

-12m + 12m =0

Step-by-step explanation:

Given

Initial\ Position = -12m

Rise = 12m

Required

Represent as an equation

The new position of the hook is calculated by:

New\ Position = Initial\ Position + Rise

This gives:

New\ Position = -12m + 12m

New\ Position = 0

Hence, the equation is:

-12m + 12m =0

3 0
3 years ago
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