We have the equation
Let's complete the square, to do it let's add and subtract 25 on the right side
Now we can have y in function of x
Now we can already identify the vertex because it's in the vertex form:
Where the vertex is
As we can see, h = 5 and k = -2, then the vertex is
Now we can continue and find the focus, the focus is
We have a = 1/20, therefore
The focus is
And the last one, the directrix, it's
Then
Hence the correct answer is: vertex (5, -2); focus (5, 3); directrix y = -7
Expression 4 (3n - 5) is equivalent to <em><u>C: 12n - 20</u></em>
<h3>Further explanation </h3>Algebraic expressions in mathematics are a combination of coefficients, numbers, variables, constants and arithmetic operations such as addition, subtraction, multiplication, and division.
The main composition of algebraic expressions are:
algebraic forms separated by arithmetic operations
consists of one phrase (monomial) to many phrases (polynomial)
is a value that can be changed, can be in the form of letters, for example, x, y, a, b, etc.
is a fixed value, can be a number
Calculation operations include multiply, divide, add, substract, etc.
There are several properties in integer multiplication operations
Multiplication between integers will produce integers too
a x b = b x a
ax (bxc) = (axb) xc
ax1 = 1 x a = a
*<em> addition </em>
ax (b + c) = axb + axc
* <em>substraction </em>
ax (b-c) = axb - axc
We can use distributive property of <em>substraction </em>to solve the problem
"Equivalent to" means having the same value.
From the answer choices , which produce the same expression is C. 12n-20
<h3>Learn more </h3>6 squared divided by 2 (3) +4
an algebraic expression
Keywords: PEMDAS, arithmetic operations, multiply, Parentheses, equivalent to
