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
kvv77 [185]
3 years ago
12

Find the focus and the directrix of the parabola with the equation y = 1∕4(x – 6)2+ 5

Mathematics
1 answer:
strojnjashka [21]3 years ago
5 0

Answer:

B)

Focus = (6,6), directrix is y = 4

Step-by-step explanation:

A parabola is the locus of a point that is equidistant from a fixed line (known as directrix) and a fixed point (known as focus).

The equation of a parabola in vertex form is given as:

y=a(x-h)^2+k

It can be further simplified to:

(x-h)^2=4p(y-k)

The directrix of this parabola is given at line y = k - p and the focus is at (h, k + p)

Given that:

y = \frac{1}{4}(x-6)^2+ 5 \\(y-5)=\frac{1}{4}(x-6)^2\\(x-6)^2=4(y-5)

Comparing (x-6)² = 4(y-5) with (x-h)² = 4p(y-k), It can be gotten that h = 6, p =1 and k = 5

The directrix of this parabola is given at line y = k - p = 5 - 1 = 4 and the focus is at (h, k + p) =  (6, 5+1) = (6, 6)

Focus = (6,6), directrix is y = 4

You might be interested in
How do you determine whether to use substitution or elimination. give an example of a system that you would solve using each met
nadezda [96]
You determine which one to use by seeing which one would be easier

elimination: 5x + 7y = 2
                  -5x + 6y = 6

substitution: y = 9x + 5
                  2y = 7x + 2
3 0
3 years ago
Give a real world example where being able to solve a quadratic equation might be useful. Be very specific and tell how the equa
WINSTONCH [101]
Real life problem for quadratic equation:

A ball is thrown into the air from the edge of a building, 50 feet above ground. It’s initial velocity is 20 feet per second. About how long does it take for the ball to hit the ground?

Sorry if this doesn’t help.
5 0
3 years ago
Contestant and like terms. What do they mean?
ICE Princess25 [194]

Answer:

Step-by-step explanation:

Like Terms: terms that have the same variable raised to the same power. So like 5x plus 5x plus 5. 5x and 5x are like terms.

I'm going to assume you mean Constant instead of contestant so

Constant: Terms without variables

Example: 5x+2x+7

5x and 2x are like terms

7 is a Constant

8 0
3 years ago
Angle G and H are vertical angles. If angle G is 45 degrees and angle H is 2x degrees, what is the value of x?
Veseljchak [2.6K]

Answer:

x = 22.5

Step-by-step explanation:

Vertical angles are congruent by the vertical angles theorem. Therefore is angle G is 45 degrees, then that means that angle H must be 45 degrees as well.

The value of x can be found by making the expression that represents angle H (2x) equal to 45 in an equation to solve for x.

2x = 45

Divide both sides by 2.

x = 22.5

6 0
3 years ago
PLEASE HELP .!!! ILL GIVE BRAINLIEST.. *EXRTA POINTS* .. DONT SKIP :(( ! <br> ILL GIVE 40 POINTS .
alexira [117]

Answer:

x=1 y=2.5

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Ryan buys a clock for $75 and sells it for $100. what is the percent profit
    13·2 answers
  • Translate the word phrase into a variable expression. Five more than the product of x and 6. A. (x + 6) + 5 B. 5x + 6 C. 6x + 5
    6·2 answers
  • It takes_ hours to reach the sea.
    6·2 answers
  • The following data set lists average life span(in years) of 16 different animals found in Africa.
    9·1 answer
  • Simplify -3sqrt2 + 3sqrt8.<br><br> A. 9sqrt2<br> B. 0<br> C. 3sqrt2<br> D. -3sqrt2
    11·2 answers
  • The radius of a circle is 3 cm. find the area in terms of pi​
    13·2 answers
  • Help please ?.........
    12·1 answer
  • Find the length of segment GH.
    5·2 answers
  • What is the 10th term of the series 4,13,22,31
    8·2 answers
  • Solve the inequality 9.5+6x&gt;=42.1
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!