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
Alika [10]
3 years ago
13

Find the x-intercepts of the parabola with

Mathematics
1 answer:
lutik1710 [3]3 years ago
6 0

Answer:

The x-intercept are (-7 , 0) and (5 , 0)

Step-by-step explanation:

* Lets revise the general form of the equation of the parabola

- The general form of the equation of the parabola is:

  y = ax² + bx + c , a , b , c are constant

- The y-intercept is c, because the parabola intersect the y-axis at

  point (0 , c)

- The x-coordinate of the vertex point is -b/2a

* Now lets solve the problem

∵ The general form of the equation of the parabola is y = ax² + bx + c

∵ The y-intercept is -105

∴ c = -105

∴ y = ax² + bx - 105

∵ The vertex point is (-1 , -108)

∴ The x-coordinate of the vertex of the parabola = -1

∵ The x-coordinate of the vertex of the parabola = -b/a

∴ -b/2a = -1 ⇒ using cross multiplication

∴ -b = -2a ⇒ multiply two sides by -1

∴ b = 2a

- Substitute the value of b in the equation

∴ y = ax² + 2ax - 105

- Substitute the value of x , y in the equation by the coordinates of

 the vertex point

∵ The vertex point lies on the parabola

∴ put x = -1 and y = -108

∴ -108 = a(-1)² + 2a(-1) - 105

∴ -108 = a - 2a - 105 ⇒ add the like term

∴ -108 = -a - 105 ⇒ add 105 to both sides

∴ -3 = -a ⇒ multiply both sides by -1

∴ a = 3

- Substitute the value of a in the equation

∵ y = ax² + 2ax - 105

∴ y = 3x² + 2(3)x - 105

∴ y = 3x² + 6x - 105

- To find the x-intercept put y = 0

∴ 3x² + 6x - 105 = 0

- All the terms have 3 as a common factor

∴ divide all the terms by 3

∴ x² + 2x - 35 = 0

- Now factorize it into two factors

∵ x² = x × x ⇒ the 1st term in the bracket and the 1st term in the

  2nd bracket

∵ -35 = -5 × 7 ⇒ the 2nd term in the 1st bracket and the 2nd term in the    

  2nd bracket

∵ x × - 5 = -5x ⇒ means

∵ x × 7 = 7x ⇒ extremes

∵ 7x - 5x = 2x ⇒ the middle term

∴ (x - 5)(x + 7) = 0

- Equate each bracket by 0

∴ x - 5 = 0 ⇒ add 5 to both sides

∴ x = 5

OR

∴ x + 7 = 0 ⇒ subtract 7 from both sides

∴ x = -7

∴ The x-intercept are -7 , 5

* The x-intercept are (-7 , 0) and (5 , 0)

You might be interested in
What number is 7 units to the left of -1?<br><br> 8<br> 6<br> -8<br> -6
Viefleur [7K]

Answer:

7 <u>units to the left is -6 </u>

Step-by-step explanation:

your counting back wards but its not a neg. its positive so the answer is 6

4 0
3 years ago
AGGGGGGGG!!! I'm so bad at math!! HELLLPPPLL
AlekseyPX
The correct answer is B. Hope it helps!
8 0
3 years ago
The sum of 4X and 2X is less than the difference of 5X and 13
eduard

Answer: 5x-13-(4x+2x)

Step-by-step explanation:

6 0
3 years ago
What is the equivalent decimal for -1.25
Tanzania [10]
I honestly do not know what to say here: it's already in decimal form. Please, if you made a mistake while typing in the problem, tell me.
4 0
3 years ago
Read 2 more answers
Help
enyata [817]
Part A=5 inches 
Part B=6.25 
I know part A but not sure I think thats the answer for part B
4 0
3 years ago
Other questions:
  • Does anyone know these answers
    6·1 answer
  • A pizza company makes pizza in three different sizes: small, medium, large. There are four possible toppings: pepperoni, sausage
    5·1 answer
  • Lines b and c are parallel. What is the measure of Angle6?
    13·1 answer
  • Three less than 11 times a number
    14·1 answer
  • Determine how much it would cost to buy 7 bottles from krokers market
    5·1 answer
  • 6. About 0.8% of the land in Maine is federally owned. If
    15·1 answer
  • 20 points plus that brain thing
    8·1 answer
  • Se quiere realizar la adición y multiplicación de los números enteros 43 y -32. En relación con los signos de las operaciones se
    9·1 answer
  • PLSSS HELP IF YOU TURLY KNOW THISS
    10·2 answers
  • ( Need answered fast please)What is the value of c?<br> c<br> c–35°<br> c–50°
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!