MATHEMATICS HIGH SCHOOL

The standard form of the equation of a parabola is y = 5x2 + 20x + 14. What is the vertex form of the equation?

A. y = 5(x + 2)2 + 10
B. y = 5(x + 2)2 - 6
C. y = 5(x + 4)2 - 6
D. y = 5(x + 4)2 + 10

Answers

Answer 1
Answer: The vertex form of quadratic equation is expressed as:

y = a (x - h)² + k

We manipulate the given equation to be the same as the vertex form. First we transpose the constants to the left-hand side.

y - 14 = 5x² + 20x

Then, we factor out in right hand side the coefficient of the x² term.

y- 14 = 5 (x² + 4x)

We divide the coefficient of the x term with 2 and take its square. We add this value to both sides of the equation but we should remember that in the left-hand side we should multiply this value with five to keep it balanced.

y - 14 + 20 = 5 (x² + 4x +4)

We simplify the right-hand side as:

y + 6 = 5 (x + 2)²

We can now manipulate further the equation above in the vertex form. Thus,

y= 5 [ x- (-2)]² - 6
Answer 2
Answer:

Answer:

y = 5(x+2)^2 - 6

Step-by-step explanation:

Related Questions

The legs of an isosceles triangle are 0.3 foot less than twice the base. The perimeter of the triangle is 4.9 feet.What is the length of one of the triangle’s legs?
A six sided die, with sides numbered 1,2,3,4,5, and 6, is tossed. What is the probability of tossing a number less than 3
Solve for n in the literal equation2x+n=t
The movie theatre has 250 seats. 225 seats were sold for the current showing . What percent of the seats are empty?
Ken drew a pair of intersecting rays and marked the angle between them.Which of these statements best compares the pair of intersecting rays with the angle?-The rays and the angle have two endpoints each.-The rays and the angle have their lines extending in opposite directions.-The rays have a number of points lying on them and the angle has only one point lying on it.-The rays extend infinitely and the angle is made by the rays which have a common endpoint....?

A night at the Barefoot Cay Resort in Roatan, Honduras costs 3,915 Honduran Lempiras. Given that 1 U.S. dollar (USD) is worth 21.4 Honduran Lempiras (HL),what is the equivalent cost in U.S. dollars? Round your answer to the nearest dollar.
Choose the TWO fractions that are multiplied together to calculate the solution using dimensional analysis. Make sure that the units of the fractions you choose
cross-cancel to produce the unit of your desired answer. You must have the correct two fractions selected at the same time to get credit when you
check your answer. You get two attempts to check your answer.
0
1 USD
21.4 HL
21.4 HL
1 USD
1
3915 HL
3915 HL O.
1

Answers