All categories

3 years ago

Two sets of quadratic expressions are shown below in various forms:

Mathematics

2 answers:

Elan Coil [88]3 years ago

6 0

Solution:

1. $x^2 + 3 x +2= x^2 + 2 x + x + 2= x(x+2)+1(x+2)=(x+1)(x+2)\\\\ x^2 + 3 x + 2=(x+\frac{3}{2})^2-(\frac{3}{2})^2+2=(x+\frac{3}{2})^2-2.25+2=(x+\frac{3}{2})^2-0.25$

2. $x^2 + 5 x + 6 =x^2+ 3 x + 2 x+6=x(x+3)+2(x+3)= (x + 2)(x + 3)\\\\ x^2 + 5 x + 6 =(x+\frac{5}{2})^2-(\frac{5}{2})^2+6=(x+\frac{5}{2})^2-6.25+6=(x+\frac{5}{2})^2-0.25$

Line 1: x² + 3 x + 2= (x + 1)(x + 2)= (x + 1.5)² − 0.25 contains three equivalent expressions.

Ray Of Light [21]3 years ago

3 0

Line one is equivalent

You might be interested in

Graft the solution to the inequality on the number line. m>2.8

Oduvanchick [21]

Answer:

See the graph of the given inequality in the attachment as shown below:

Step-by-step explanation:

Given the inequality: $m > 2.8$

To graph this inequality on the number line.

Remember:

If the symbol is $(\geq or \leq)$ then you fill in the dot

If the symbol is $(> or$ then you do not fill in the dot.

Since, in the given inequality the symbol is '>'

Now, sketch a number line and draw an open circle around the number 2.8.

You can see the number line as shown below in the attachment.

4 0

3 years ago

Read 2 more answers

1. A football team gains 2 yards on the first play,

Ilya [14]

Option C

The football team had a overall loss of 2 yards

Solution:

When the team gains yards we use a positive value, and when the team loses yards we use a negative value.

Given that, football team gains 2 yards on the first play

First play = +2

Given that football team loses 5 yards on the second play

Second play = -5

Given that football team loses 3 yards on the third play

Third play = -3

Given that football team gains 4 yards on the fourth play

Fourth play = +4

Put the yards from four plays together, we get

⇒ 2 -5 -3 + 4

Let us simplify

⇒ -3 -3 + 4 = -6 + 4 = -2

So, -2 represents loss of two yards (since negative value indicates loss)

3 0

3 years ago

Writing an equation of a probably given the vertex and focus

White raven [17]

The equation of the vertical parabola in vertex form is written as

$y=\frac{1}{4p}(x-h)^2+k$

Where (h, k) are the coordinates of the vertex and p is the focal distance.

The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.