1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
balu736 [363]
3 years ago
10

Consider the given quadratic equations. Equation A Equation B Equation C Equation D y = 3x2 − 6x + 21 y = 3x2 − 6x + 18 y = 3(x

− 1)2 + 18 y = 3(x − 1)2 + 21 Complete the following statement. Equations are equivalent, and of those, equation is in the form most useful for identifying the extreme value of the function it defines.

Mathematics
2 answers:
8_murik_8 [283]3 years ago
7 0

Answer:

  Equations A and C are equivalent, and of those, equation C is in the form most useful ...

Step-by-step explanation:

In standard form, the equations are ...

Equation A: y = 3x² -6x +21

Equation B: y = 3x² -6x +18

Equation C: y = 3x² -6x +21 . . . . equivalent to A

Equation D: y = 3x² -6x +24

__

Equation C is in vertex form, so the vertex (extreme value) can be read directly from the equation. It is (x, y) = (1, 18).

Equations A and C are equivalent; equation C is most useful for finding the vertex.

Vlada [557]3 years ago
7 0

Answer with explanation:

→→Two equations or two polynomials are said to be equivalent, if written in distinct ways, and real value of variables is substituted in both equivalent and Original Polynomial, the numerical value of both the polynomials are Same.

→→The four Quadratic Polynomials are:

1.\text{Equation} A: y = 3x^2 - 6 x + 21\\\\2.\text{Equation} B: y = 3x^2 - 6 x + 18\\\\3.\text{Equation} C: y = 3(x-1)^2 +18=3(x^2-2 x +1)+18\\\\y=3x^2 - 6 x +18+3\\\\y=3x^2 - 6 x +21\\\\3.\text{Equation} C: y = 3(x-1)^2 +21

→→If you will look at Equation A and Equation C, both the equation are Quadratic, Coefficient of x², Coefficient of x, as well as , constant term is same in both the equation.So, Equation A, and Equation C, are equivalent.

→→If you will look at the function,

y=3\times (x-1)^2+18\\\\y-18=3\times(x-1)^2

at, x=1, y=18, which is extreme value of the function, as at vertex of the parabola , Parabola attains it's Maximum value.

⇒⇒Equations A and C,

[1.\text{Equation} A: y = 3x^2 - 6 x + 21\\\\3.\text{Equation} C: y = 3(x-1)^2 +18]

are equivalent, and of those, equation is in the form most useful for identifying the extreme value is 3.\text{Equation} C: y = 3(x-1)^2 +18]  function it defines.

You might be interested in
Select the choice that translates the following verbal phrase correctly to algebra: y less than 21
Romashka [77]
Y (y) less than (minus) 21 (21
y-21
3 0
3 years ago
Read 2 more answers
I need help on this one.number
bonufazy [111]
6 inches x 8 inches = 48 inches

48 inches x 1.5 feet = 72 feet

72 feet x $9.75 = $702 <-- Total

Answer $720
8 0
3 years ago
Use the graph of y = -x2 - 2x + 3 to solve
Anna007 [38]
Explanation:
y
+
2
x
=
3

y
=
−
2
x
+
3

When
x
=
0
, y-intercept
=
3
coordinates
(
0
,
3
)

When
y
=
0
, x-intercept
=
3
2
coordinates
(
3
2
,
0
)

Knowing two points, we can draw the graph.
graph{-2x + 3 [-10, 10, -5, 5]}
Answer
7 0
2 years ago
On a piece of paper, draw two lines so that the vertical angles formed are supplementary.
weeeeeb [17]
Supplementary angles are two angles whose sum equal to 180 degrees. Vertical lines are the opposite angles in the intersecting lines. Thus, each of your angles must be 90 degrees. Just simply draw two straight and intersecting lines. 

3 0
3 years ago
Read 2 more answers
This graph relates the volumes of triangular pyramids with a base area of 12 square inches and their heights.
Nikolay [14]

Answer:

V=40\ in^3

Step-by-step explanation:

The graph is not attached, however we know that, the volume of a triangular pyramid is given by the formula

V=\frac{1}{3}Bh

where

B is the area of the triangular face

h is the height of the pyramid

we have

B=12\ in^2\\h=10\ in

substitute the given values

V=\frac{1}{3}(12)(10)=40\ in^3

3 0
3 years ago
Other questions:
  • What is the slope of a line that is perpendicular to the line y = -1/2 x + 5?
    15·1 answer
  • Find the GCF of the first two terms and the GCF of the last two terms of the polynomial. 5h^3+20h^2+4h+16
    9·1 answer
  • What is the measure of AC?
    9·2 answers
  • What is the product 5/10 x 10/3 ​
    13·2 answers
  • Is 7/11 a rational number
    15·2 answers
  • Jackie wants to buy a new CD player. It costs $32.95. She has saved $26 and has a new coupon for %30 off the price. Does Jackie
    6·2 answers
  • Adam's music playlist contains songs he bought and songs his mother bought. The ratio of his songs to his mother's songs is 5:3.
    15·1 answer
  • Solve the equation for c<br> M+3c=8
    14·2 answers
  • Is -2/7 a natural number whole number integer rational number irrational number or real number
    11·2 answers
  • Select the equation that most accurately depicts the word problem.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!