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
PIT_PIT [208]
2 years ago
7

Find the equations of the tangents to the curve y = x²-x-12 at each of the points where the curve crosses the x-axis.​

Mathematics
1 answer:
poizon [28]2 years ago
6 0

Step-by-step explanation:

First, find the zeroes of the parabola

{x}^{2}  - x - 12

{x}^{2}  - 4x + 3x - 12

x(x  - 4) + 3(x - 4)

(x +  3)(x  - 4) = 0

x =  - 3

x - 4 = 0

x = 4

So the zeroes or where the curve crosses the x axis is at 4 and -3.

Now, we take the derivative of the function.

\frac{d}{dx} ( {x}^{2}  - x - 12) = 2x - 1

Plug in -3, and 4 into the derivative function

2( - 3) =  - 7

2(4) - 1 = 7

So at x=-3, our slope of the tangent line is -7 and must pass through (-3,0). So we use point slope formula.

y - y _{1} = m(x - x _{1})

y - 0 =  - 7(x - (  - 3)

y =  - 7x - 21

At x=4, our slope of tangent line is 7, and pass through (4,0) so

y - 0 = 7(x - 4)

y = 7x - 28

So the equations of tangent is

y =  - 7x - 21

y = 7x - 28

You might be interested in
What does this mean?
boyakko [2]

Answer:

Its the symbol "pi" which is 3.14

3 0
3 years ago
Read 2 more answers
-47=x+15 solve the equation
myrzilka [38]
-47 = x + 15
Rearrange it to isolate x:
-47 - 15 = x
-62 = x
5 0
3 years ago
Read 2 more answers
Consider the given function.
Natali5045456 [20]

Answer:

D)

Step-by-step explanation:

f(x) = x^2 -14x -72

0=x^2 - 14x-72

0=x^2 - 18x+4x-72

0=x(x-18)+4(x-18)

0=(x-18)(x+4)

x-18=0 or x+4=0

x1=18 or x2=-4

asis of symmetry: x=(x1+x2)/2

x=(18+(-4))/2

x=14/2

x=7

3 0
3 years ago
You guys know what Sawcon is?
vagabundo [1.1K]
Yeah I know why ?????,????
6 0
3 years ago
Read 2 more answers
The maximum capacity of the school auditorium is 420 people. Write an inequality for the situation. Tell what type of numbers th
posledela
The number of people in the auditorium can be less than or equal to 420 so let p represent the number of people
The inequality is p≤420
4 0
3 years ago
Other questions:
  • What are the solutions to the quadratic equation x^2-16=0
    12·1 answer
  • What is true about the radius and diameter of the circle whose diameter is 50 mm ?
    14·1 answer
  • What common base can be used to rewrite each side of the equation 2^(x+3)-3=5
    12·2 answers
  • Maya purchased a prepaid phone card for $25. Long distance calls cost 23 cents a minute using the card. Maya used her card only
    13·1 answer
  • FOR BRAINLIEST
    12·2 answers
  • Please help!! 30 points
    6·1 answer
  • The triangular prism shown has ? triangular face(s) and ? lateral face(s).
    8·1 answer
  • What is the area of the balcony shown below
    14·2 answers
  • 24 students in a class took an algebra test. If 18 students passed the test what percent passed?
    11·2 answers
  • Pls pls pls help me I didn’t understand
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!