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2 years ago

What is the equation of this parabola in vertex form

Mathematics

1 answer:

attashe74 [19]2 years ago

6 0

first off, let's notice the parabola is a vertical one, therefore the squared variable is the x, and the parabola is opening upwards, meaning the coefficient of x² is positive.

let's notice the vertex, or U-turn, is at (-2, 2)

$\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \boxed{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{-2}{ h},\stackrel{2}{ k}) \\\\\\ y=+1[x-(-2)]^2+2\implies y=(x+2)^2+2$

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John and Liz are sharing a large pizza. John ate 2/3 of the pizza, and Liz ate 1/4 of the pizza. How much of the pizza is left?

Mkey [24]

Add what they ate
2/3 + 1/4 =
11/12
Then subtract that from the whole pizza
12/12 - 11/12 =
1/12
1/12 of the pizza is left

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2 years ago

Function Notation - Function Machines

stepan [7]

The function notation of the following are:

f(1) = 5

f(0) = 1

f(-3) = -11

f(8) = 33

Given:

x is the input.

the function is 4x+1

f(x) is the output.

we are asked to determine the values of the following :

a. f(1)

x = 1

so f(x) = 4x+1

f(1) = 4(1)+1

f(1) = 4+1

f(1)=5

b. f(0)

x = 0

so f(x) = 4x+1

f(0) = 4(0)+1

f(0) = 0+1

f(0)=1

c. f(-3)

x = -3

so f(x) = 4x+1

f(-3) = 4(-3)+1

f(1) = -12+1

f(1)= -11

d. f(8)

x = 8

so f(x) = 4x+1

f(8) = 4(8)+1

f(8) = 32+1

f(1)=33

Hence we get the required values.

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7 0

10 months ago

50 points!!!! What is the area of the trapezoid

Deffense [45]

Answer:

308 square feet

Step-by-step explanation:

A = 1/2 (26+18) (14)

A = 1/2 (44) (14)

A = 308

Answer

308 square feet

4 0

2 years ago

Read 2 more answers

What is the sum of the expressions for n=-2n=−2 and m=5m=5 ?

Liula [17]

Answer:

- 43

Step-by-step explanation:

Expression: (3m+2n−6) and (−4−6m+7n)

n= -2 and m=5

Before inserting the values, let's add both expressions.

(3m+2n−6) + (−4−6m+7n)

3m+2n−6 −4 − 6m + 7n

-3m + 9n - 10

Inserting the values;

-3(5) + 9(-2) - 10

-15 - 18 -10

- 43

6 0

2 years ago

Which of the following equations have complex roots?

mestny [16]

Answer:

Step-by-step explanation:

Complex roots of quadratic functions occur when the <u>discriminant is negative</u>.

<u>Discriminant</u>

$b^2-4ac\quad\textsf{when}\:\:ax^2+bx+c=0$

Evaluate the discriminant of each of the given equations.

$\textsf{A.} \quad 3x^2+2=0$

$\implies a=3, \quad b=0, \quad c=2$

$\implies b^2-4ac=0^2-4(3)(2)=-24$

As -24 < 0 the equation will have complex roots.

$\textsf{B.} \quad 2x^2+1=7x$

$\implies 2x^2-7x+1=0$

$\implies a=2, \quad b=-7, \quad c=1$

$\implies b^2-4ac= (-7)^2-4(2)(1)=41$

As 41 > 0 the equation does not have complex roots.

$\textsf{C.} \quad 3x^2-1=6x$

$\implies 3x^2-6x-1=0$

$\implies a=3, \quad b=-6, \quad c=-1$

$\implies b^2-4ac=(-6)^2-4(3)(-1)=48$

As 48 > 0 the equation does not have complex roots.

$\textsf{D.} \quad 2x^2-1=5x$

$\implies 2x^2-5x-1=0$

$\implies a=2, \quad b=-5, \quad c=-1$

$\implies b^2-4ac=(-5)^2-4(2)(-1)=33$

As 33 > 0 the equation does not have complex roots.

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1 year ago