All categories

3 years ago

the standard form of the equation of a parabola is y=x^2 + 4x + 11. What is the vertex form of the equation?

Mathematics

2 answers:

Margaret [11]3 years ago

7 0

Answer:

y = (x + 2)² + 7

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square.

add/ subtract (half the coefficient of the x term )²

y = x² + 4x + (2)² - (2)² + 11

= x² + 4x + 4 - 4 + 11

= (x + 2)² + 7 ← in vertex form

Harman [31]3 years ago

3 0

y=x²+4x+11

y=(x²+2(2) (x) +2²) +11-2²

y=(x+2) ²+7

You might be interested in

Which of the following equations represents the greatest value of x?

Nutka1998 [239]

Solve for x to determine which equation represents the greatest value for x.

Equation 1

$x^2 = 17$

$x$ ≈ $4.12$

Equation 2

$x^2 = 26$

$x$ ≈ $5.1$

Equation 3

$x^3 = 64$

$x=4$

Equation 4

$x^3 = 27$

$x=3$

Answer: Equation 2

7 0

3 years ago

18) If the straight line y=m X touches the circle (x - 2)^2 + (y - 6)^2 = 4, then m= ......

fenix001 [56]

Answer:

(8) d. 4/3 (9) a. (X - 4)^2 + (y-4)^2= 25

Step-by-step explanation:

8. CENTER OF CIRCLE: O (2,6)

radius of circle : r = √4 = 2

if m = 4/3 line: y = 4/3 x

perpendicular distance (d) from center of circle to line y = 4/3 x is

d = |((4/3 x 2) + (-1) x 6)| / √((4/3)² + (-1)²) = |(-10/3)| / √(25/9) = (10/3) / (5/3) = 2

d = r means line touch with circle

9. center of circle is the intersection of the diagonals of rectangle (4,4) and its radius is 5 (illustrated)

the equation of circle: (X - 4)^2 + (y-4)^2= 25

8 0

3 years ago

eugene wants to buy jeans at a store that is giving $10 off everything. the tav on the jeans is marked 50% off. the original pri

Kipish [7]

<span>Eugene wants to buy jeans at a store that is giving $10 off everything.
Now, the tav on the jeans is marked 50% off and the original price is $49.98.
Let’s find the total cost if the 50% discount is applied before the $10 discount
Solutions:
=> 49.98 dollars * .50 = 24.99
Subtract this to get the answer:
=> 49.98 – 24.99 = 24.99 dollars, this is now that price of the jeans before 10 dollars discount is applied.</span>

4 0

3 years ago

Read 2 more answers

Find the four real zeros of the polynomial. f(x) = x4 + 6x3 - 3x2 -52x - 60

OLEGan [10]

The function is

$f(x)=x^4+6x^3-3x^2-52x-60$

The "zeros" of a function, are the values of x, for which f(x)=0

According to the "Rational Root Theorem", the rational roots of f, are factors of 60.

That is, when trying to find the roots of a polynomial function, it is a very good idea to first check the factors of the constant term.

All numbers shown in the choices are factors of 60, so we will solve the problem by trial:

$f(2)=2^4+6\cdot2^3-3\cdot2^2-52\cdot2-60=16+48-12-104-60 \neq 0$

2 is not a root, so we eliminate choices A and D,

Choices B and C are almost equal, with only 1 different number, so let's check whether 5 is a root or not:

$f(5)=(5)^4+6\cdot(5)^3-3\cdot(5)^2-52\cdot(5)-60$

$=625+750-75-160-60=60$

but

$f(-5)=(-5)^4+6\cdot(-5)^3-3\cdot(-5)^2-52\cdot(-5)-60$

$=625-750-75+160-60=0$

So the right choice is B

7 0

4 years ago

The local store where Tim shops charges a 7% sales tax for clothing. Complete the table by figuring the cost of the jeans after

Sindrei [870]

Answer:

$A=P+P\times S\%$

Step-by-step explanation:

For calculating the sales tax of a product, it is required to first multiply the original cost price of the product by the sales tax percentage.

Once the sales tax has been computed add it to the original cost price in order to determine the total cost of the product.

The formula of final amount is:

$A=P+P\times S\%$

Here,

A = final amount

P = original cost price

S = sales tax percentage

7 0

3 years ago