1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Angelina_Jolie [31]
3 years ago
11

How do you write a quadratic function in vertex and standard form

Mathematics
1 answer:
Marta_Voda [28]3 years ago
3 0

Answer:

  • vertex form: f(x) = a(x -h)^2 +k
  • standard form: f(x) = ax^2 +bx +c

Step-by-step explanation:

Often, you're given one form and asked to write the equation in the other form. Here, we can show the relationship between the two forms.

In <u>vertex form</u>, the vertex of the function (h, k) is obvious in the way the function expression is written:

  f(x) = a(x -h)^2 +k . . . . . . . for vertex (h, k) and vertical scale factor "a"

If we "simplify" this form, we get ...

  f(x) = a(x^2 -2hx +h^2) +k

  f(x) = ax^2 -2ah + (ah^2 +k) . . . . . "standard form" from vertex form

Comparing this to standard form, we can see the relations between the coefficients are ...

  • a = a
  • b = -2ah
  • c = ah^2 +k

__

In <u>standard form</u>, terms are written in descending order of the exponent of the variable.

  f(x) = ax^2 +bx +c

Generally, coefficients are named in alphabetical order, starting with "a" for the leading coefficient (the coefficient of the highest-degree term).

We can use the relations shown above to find the vertex from from these coefficients.

  b = -2ah

  h = -b/(2a) . . . . . divide by the coefficient of h

And the other coefficient of the vertex is ...

  k = c - ah^2 . . . . subtract ah^2 from the equation for c

  k = c - b^2/(4a)

Then ...

  f(x) = a(x +b/(2a))^2 +(c -b^2/(4a)) . . . . . "vertex form" from standard form

_____

You may notice that the key relationship is that between "b" and "h". It is useful to remember it:

  h = -b/(2a)

You might be interested in
The radius of the cone is 7 in and y = 25 in. What is the volume of the cone in terms of π? A cone with a right triangle formed
Lady bird [3.3K]

Answer:

142.1π in³

Step-by-step explanation:

Given that:

The radius (r) =  7 in

The slant height (y) = 25 in

Then the height (x) can be determined by using the Pythagoras rule:

y² = x² + r²

25² = x² + 7²

125 = x² + 49

125 - 49 = x²

x² = 76

x = √76

x = 8.7

The formula for the volume of a cone is;

= 1/3 πr²h

where;

height(h) is calculated as "x" from above = 8.7

Then;

= 1/3 × π × (7 in)² × 8.7 in

= 142.1π in³

5 0
3 years ago
Read 2 more answers
URGENT!! Which line if graphed would be steepest?
GaryK [48]

Answer:

5x + 2

Step-by-step explanation:

it has the greatest slope

7 0
3 years ago
Read 2 more answers
What is the slope of the table? <br><br> What is the y-intercept of the table?
mel-nik [20]
Slope=2
Y-intercept=12



7 0
3 years ago
Use the given graph to determine the limit, if it exists.
Aleksandr-060686 [28]
As x approaches 3 from the right, the limit is 3.  There is a closed hole up there AT x=3 y=7, but we don't care about what happens AT x=3, only what happens as x APPROACHES 3. 
6 0
3 years ago
What is the probability of not getting a blue<br> on this spinner? Be sure to reduce.<br> [?]
exis [7]

Answer:

5/8

Step-by-step explanation:

The probability of not getting blue can be found by dividing the number of sections that are not blue by the total number of sections.

P(not blue)= not blue / total

There are a total of 8 sections. 3 are blue, which leaves 5 that are not blue (1 yellow, 2 red and 2 green).

not blue= 5

total= 8

P ( not blue)= 5/8

This fraction cannot be reduced, therefore our answer is 5/8

6 0
3 years ago
Other questions:
  • Eva spent $11.61 downloading songs, each song cost $1.29. Four students wrote and solved equations to find s, the number of song
    11·2 answers
  • The number of pages in the books in a library follow a normal distribution. The mean number of pages in a book is 150 with a sta
    15·1 answer
  • George found that he blinked 85 times in 15 minutes. At this rate, how many seconds passed during 51 blinks?
    10·1 answer
  • A collection of 35 DVD movies he received eight of them has given as a gift ​
    14·1 answer
  • Find the sum of the geometric series.
    13·1 answer
  • If a 12-meter-tall airplane hangar casts a 18-meter shadow at the same time a parked jet casts a 6-meter shadow , how tall is th
    13·1 answer
  • Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest fo
    7·1 answer
  • Write in point-slope form an equation of the line that passes through the point (3,0) with slope 23.
    15·1 answer
  • You randomly choose two shapes from the bag, with replacement. Find the probability of choosing a star and then a circle. Write
    7·1 answer
  • ??????????????????????
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!