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Nonamiya [84]
3 years ago
7

What form do we place a quadratic in to find the Vertex, or "extrema” of a quadratic function?​

Mathematics
1 answer:
pychu [463]3 years ago
8 0

Answer:

The vertex form of the quadratic function, f(x) = a·(x - h)² + k

Step-by-step explanation:

The general form of a quadratic function is given as follows;

f(x) = a·x² + b·x + c

The vertex form of the quadratic function is f(x) = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex of the parabola

h = -b/2·a, k = f(h)

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A rectangle has a height of t^2+7t+6t
jek_recluse [69]

Answer:

2t^3+15t^2+19t+6

Step-by-step explanation:

Height of the Rectangle=t^2+7t+6

Width of the Rectangle=2t+1

Area of the Rectangle = Height X Width

=(2t+1)(t^2+7t+6)\\=2t(t^2+7t+6)+1(t^2+7t+6)\\=2t^3+14t^2+12t+t^2+7t+6\\$Collect like terms\\=2t^3+14t^2+t^2+12t+7t+6\\Area=2t^3+15t^2+19t+6\\

The area of the rectangle is 2t^3+15t^2+19t+6

4 0
3 years ago
Used use euler's method with step size 0.1 to estimate y(0.5), where y(x) is the solution of the initial-value problem y ' = y +
brilliants [131]
We want to solve the Initial Value Problem y' = y + 4xy, with y(0) = 1.

To use Euler's method, define
y(i+1) = y(i) + hy'(i),  for i=0,1,2, ..., 
where
h = 0.1, the step size.,
x(i) = i*h

1st step.
y(0) = 1 (given) and x(0) = 0.
y(1) ≡ y(0.1) = y(0) + h*[4*x(0)*y(0)] = 1 

2nd step.
x(1) = 0.1
y(2) ≡ y(0.2) = y(1) + h*[4*x(1)*y(1)] = 1 + 0.1*(4*0.1*1) = 1.04

3rd step.
x(2) = 0.2
y(3) ≡ y(0.3) = y(2) + h*[4*x(2)*y(2)] = 1.04 + 0.1*(4*0.2*1.04) = 1.1232

4th step.
x(3) = 0.3
y(4) ≡ y(0.4) = y(3) + h*[4*x(3)*y(3)] = 1.1232 + 0.1*(4*0.3*1.1232) = 1.258

5th step.
x(4) = 0.4
y(5) ≡ y(0.5) = y(4) + h*[4*x(4)*y(4)] = 1.258 + 0.1*(4*0.4*1.258) = 1.4593

Answer:  y(0.5) = 1.4593
4 0
3 years ago
Please help i will mark brainliest for anyone who can help me 15 points on the line
gregori [183]

Answer:

A: a^3

B: c^1 or just c

Step-by-step explanation:

Subtract the exponents

6 0
3 years ago
A rectangle is drawn on a coordinate plane. Three vertices of the rectangle are points L(−7,14) , M(9,14) , and N(9,−12) . Point
Nata [24]
(-7,-12) i believe this is correct
7 0
3 years ago
Is the relation a function?<br><br> Select Yes or No for each relation.
Lina20 [59]
Hello! There are a few things that determine whether or not something is a function. In this case, to determine whether a relation is a function, we look at the domains, which are the x-coordinates, the first number of the pair. If the number occurs in the x-coordinate for more than one pair in a relation, then it's not a function. If a number only occurs as an x-coordinate once in the relation, then it's a function. In other words, they each have only one y-coordinate in the relation. For this question, the first, second, and third relations are functions. The fourth one is not a function, because the 3 has more than one y-coordinate, so it occurs as an x-coordinate more than once. Here are the answers easier to read.

1st : yes
2nd: yes
3rd: yes
4th: no
3 0
3 years ago
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