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
pychu [463]
3 years ago
15

The standard form of the equation for a quadratic function is, with he vertex of the graph of the function at the point (p,q). t

he factored form is y=a(x-x1) (x-x2), where x1 and x2 are the x-intercepts of the graph. Express p and q in terms of x1 and x2 by expanding the factored for then completing the square. Please show work.
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
3 0

Answer:

p = ½ (x₁ + x₂)

q = a (x₁x₂ − ¼ (x₁ + x₂)²)

Step-by-step explanation:

y = a (x − x₁) (x − x₂)

Expand:

y = a (x² − x₁x − x₂x + x₁x₂)

y = a (x² − (x₁ + x₂)x + x₁x₂)

Distribute a to the first two terms:

y = a (x² − (x₁ + x₂)x) + ax₁x₂

Complete the square:

y = a (x² − (x₁ + x₂)x + ¼(x₁ + x₂)²) + ax₁x₂ − ¼ a(x₁ + x₂)²

y = a (x − ½ (x₁ + x₂))² + a (x₁x₂ − ¼ (x₁ + x₂)²)

Therefore:

p = ½ (x₁ + x₂)

q = a (x₁x₂ − ¼ (x₁ + x₂)²)

You might be interested in
The density of glass is 2.6 g/cm3 and the density of lead is 11.3 g/cm3. Does this mean there are more particles of lead in 1 cm
Colt1911 [192]
The answer is that there are more particles in 1 cubic cm. this is because within 1 cubic cm lead has 11.3g in compared to the 2.6 glass has. m/v= density. divide the masses over the volume and that will prove your answer.
8 0
3 years ago
What is the domain of the function?
denis23 [38]
Use a calculator it's not hard
6 0
3 years ago
Helppppp meeee with thisssss
sattari [20]
X means one. so your slope is positive one and the y intercept is -5
7 0
3 years ago
Read 2 more answers
Mindy has a total of 84 candy bars in a box. If the ratio
wolverine [178]
There are 35 snickers in the box
There is also 49 Twix bars
3 0
3 years ago
Please help me with this question. :)
ladessa [460]
It would be A.
That is because you're finding out the total cost of the amount of cloves you buy, and each one costs $0.65.
3 0
3 years ago
Read 2 more answers
Other questions:
  • If the slope of y=2x+5 is changed to -2, how does the graph change?
    7·1 answer
  • What is the approximate circumference of the circle shown below
    13·1 answer
  • What is the solution set of the following equation? 1/5x^2=x-4/5
    15·1 answer
  • Delicious Donuts sells their donuts in different size packages as shown below. Which box of donuts is the better buy? *
    12·2 answers
  • C=
    15·1 answer
  • Help plsssssssddsssssssss
    11·1 answer
  • The list of ordered pairs below represents a function
    6·1 answer
  • gina sees a rectangular quilt with an area of 3,528 square inches.The length of the quilt is 72 inches. what is the width of the
    12·2 answers
  • What is the missing numerator? blank over five plus eighteen over twenty equals thirty over twenty 8 5 3 2
    13·1 answer
  • Plz help ASAP right answers only
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!