mary read 240 pages of the 400 pages in her book.what percentages of the page ls in her book did mary read?

Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?

BaLLatris [955]

Answer:

$Vertex = (\frac{1}{2},\frac{7}{4})$

Step-by-step explanation:

Given

$f(x) = x^2 - x +2$

Required

The vertex

We have:

$f(x) = x^2 - x +2$

First, we express the equation as:

$f(x) = a(x - h)^2 +k$

Where

$Vertex = (h,k)$

So, we have:

$f(x) = x^2 - x +2$

--------------------------------------------

Take the coefficient of x: -1

Divide by 2: (-1/2)

Square: (-1/2)^2

Add and subtract this to the equation

--------------------------------------------

$f(x) = x^2 - x +2$

$f(x) = x^2 - x + (-\frac{1}{2})^2+2 -(-\frac{1}{2})^2$

$f(x) = x^2 - x + \frac{1}{4}+2 -\frac{1}{4}$

Expand

$f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2 -\frac{1}{4}$

Factorize

$f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2 -\frac{1}{4}$

Factor out x - 1/2

$f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}$

Compare to: $f(x) = a(x - h)^2 +k$

$h = \frac{1}{2}$

$k = \frac{7}{4}$

Hence:

$Vertex = (\frac{1}{2},\frac{7}{4})$

8 0

3 years ago

Read 2 more answers

Jim wants to put a wallpaper border around a rectangular room. The

puteri [66]

Answer:3

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Please Help Me, I will give the person who answers the best brainliest.

lakkis [162]

The answer has to be number 2 because I took the test and I got it right

4 0

3 years ago

IMMEDIATE HELP PLS HELP NOW

irga5000 [103]

Answer:

D. y = { -x + 2 x ≥ 1}

{ x + 1 x < 1}

Step-by-step explanation:

First is to eliminate A and C, why?

This is because of the end points shown on the graph.

As shown, if you look at the point of (2,1) it is black, this means that not only is it closed but it is also means ≤ or ≥ symbol.

You are now left with B and D

The difference between these two is the symbols; they are facing the opposite directions.

While B says x ≤ 1, and x > 1

While D says x ≥ 1, and x < 1

The direction of the symbols depends on the direction of the lines and what is part of it (some what like a shaded area)

So you answer would be D

7 0

3 years ago

The length of a rectangle is 9 inches and its perimeter is 48 inches. What is the width of the rectangle?

AnnZ [28]

2x + (2)9 = 48
2x + 18 = 48
Get 2x by itself
2x = 30
x = 15

8 0

3 years ago