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2 years ago

-10

Mathematics

1 answer:

Vitek1552 [10]2 years ago

7 0

Answer:

B) -1

Step-by-step explanation:

This is the equation of a parabola which can be expressed as

y = a(x-h)² + k (1)

where (h, k) are the coordinates of the vertex which is the minimum or maximum of the graph. Strict definition is where the parabola intersects the line of symmetry ie the line which cuts a shape into half

Parabolas are symmetric around the line of symmetry

Here we see the vertex is at x = 0, y = 9 (0,9) so h=0 and k = 9

Substituting equation (1) we get

y = a(x -0)² + 9 = ax² + 9

To find a all we have to do is choose any point on the parabola, plug its x and y values into the parabola equation above

A convenient point is where the parabola intersects the positive x axis. Here x = 3 and y = 0

Plugging these values we get

0 = a(3)² + 9

a = -9/9 = -1

You might be interested in

Factor -7x^3+21x^2+3x-9 by grouping. what is the resulting expression?

Daniel [21]

Answer:

c) (3-7x^2)(x-3)

Step-by-step explanation:

-7x^3+21x^2+3x-9

Factor out a -7x^2 from the first two terms and a 3 from the last two terms

-7x^2 (x -3) +3(x-3)

Now factor out (x-3)

(x-3) (-7x^2+3)

Rearranging)

(x-3) (3-7x^2)

8 0

3 years ago

2) Kari is flying her kite at the park. She has let

Ket [755]

Answer:

approx 58 yard we can determine it by pithagoras theorem

6 0

3 years ago

John works Monday to Friday. He buys his lunch on his way to work. Each day John buys a sandwich, a bottle of water and a bag of

kipiarov [429]

Complete question

Shop A _________________ shop B £3

Any sandwich - £2.85 ___ sandwich, water crisp

A bottle of water - 60p

A bag of crisp - 85p

Answer:

£6.50, John is incorrect

Step-by-step explanation:

Number of working days = 5 = number of days meal is purchased

Total cost per meal, shop A :

£(2.85 + 0.60 + 0.85) = £4.3

Total cost for the week = 4.3 * 5 = £21.50

Total cost per meal cost Shop B = £3

Total cost for the week = 3 * 5 = £15

Difference :

£21.50 - £15 = £6.50

Hence, Amount John saves by buying from shop B is £6.50

Numbe

4 0

2 years ago

-4d + 2(3 + d) = -14<br><br> Please help

soldi70 [24.7K]

-4d + 2(3+d)= -14
distribute the 2(3+d)
-4d + 6+ 2d= -14
Combine the like terms
-4d + 2d + 6= -14
-2d + 6 = -14
subtract 6 to -14
-2d = -20
divide by -2
d= -20/-2
d= 10
Check your answer
-4(10) + 2(3+ 10) = -14
-40 + 6 + 20
-40 + 26= -14

6 0

2 years ago

Read 2 more answers

High school math. Please answer everything in picture. Thank you................................................................

vaieri [72.5K]

Answer:

3) Cubic polynomial with four terms.

4) Linear polynomial with two terms.

5) The zeros are: (1-sqrt(5))/2=-0.618, 1, and (1+sqrt(5))/2=1.618

The y-intercept is y=1

Please, see the attached graph.

6) The zeros are: -1.272, 1.272

The y-intercept is y=1

Please, see the attached graph.

7) Please, see the attached files.

8) Please, see the attached files.

9) Please, see the attached files.

10) Please, see the attached files.

Step-by-step explanation:

3) Degree is the maximun exponent that the variable "x" has, in this case 3, then this is a cubic polynomial, and it has four terms (6x^3, -7x^2, -10x, and -8).

4) Degree is the maximun exponent that the variable "x" has, in this case 1 (x=x^1), then this is a linear polynomial, and it has two terms (-10x, and 10).

5) f(x)=x^3-2x^2+1

Zeros:

f(x)=0→x^3-2x^2+1=0

Factoring:

x^3-2x^2+0x+1

! 1 -2 0 1

1 -1 -1 0

1x^2-1x -1 = x^2-x-1

x^3-2x^2+1=0→(x-1)(x^2-x-1)=0

The zeros are:

x-1=0→x-1+1=0+1→x1=1

x^2-x-1=0

ax^2+bx+c=0; a=1, b=-1, c=-1

x=(-b+-sqrt(b^2-4ac))/(2a)

x=(-(-1)+-sqrt((-1)^2-4(1)(-1))/(2(1))

x=(1+-sqrt(1+4))/2

x2=(1+-sqrt(5))/2=(1+2.236067978)/2=3.236067978/2=1.618033989=1.618

x=(1-sqrt(5))/2=(1-2.236067978)/2=-1.236067978/2=-0.618033989=-0.618

x3=(1+sqrt(5))/2

The zeros are: (1-sqrt(5))/2=-0.618, 1, and (1+sqrt(5))/2=1.618

The y-intercept is:

x=0→f(0)=(0)^3-2(0)^2+1→f(0)=0-2(0)+1→f(0)=0-0+1→f(0)=1

The y-intercept is y=1.

6) f(x)=-x^4+x^2+1

Zeros:

f(x)=0→-x^4+x^2+1=0

Factoring: Multiplyng both sides of the equation by -1:

(-1)(-x^4+x^2+1)=(-1)(0)

x^4-x^2-1=0

(x^2)^2-(x^2)-1=0

Changing x^2 by t:

t^2-t-1=0

at^2+bt+c=0; a=1, b=-1, c=-1

t=(-b+-sqrt(b^2-4ac))/(2a)

t=(-(-1)+-sqrt((-1)^2-4(1)(-1))/(2(1))

t=(1+-sqrt(1+4))/2

t1=(1+-sqrt(5))/2=(1+2.236067978)/2=3.236067978/2=1.618033989=1.618

t2=(1-sqrt(5))/2=(1-2.236067978)/2=-1.236067978/2=-0.618033989=-0.618

t^2-t+1=0→(t-1.618)(t-(-0.618))=0→(t-1.618)(t+0.618)=0

and t=x^2, then:

(x^2-1.618)(x^2+0.618)=0

Factoring the first parentheses using a^2-b^2=(a+b)(a-b), with:

a^2=x^2→sqrt(a^2)=sqrt(x^2)→a=x

b^2=1.618→sqrt(b^2)=sqrt(1.618)→b=1.272

(x^2-1.618)(x^2+0.618)=0→(x+1.272)(x-1.272)(x^2+0.618)=0

The zeros are:

x+1.272=0→x+1.272-1.272=0-1.272→x1=-1.272

x-1.272=0→x-1.272+1.272=0+1.272→x2=1.272

The zeros are: -1.272, and 1.272

The y-intercept is:

x=0→f(0)=-(0)^4+(0)^2+1→f(0)=-0+0+1→f(0)=1

The y-intercept is y=1.

3 0

3 years ago