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
tigry1 [53]
3 years ago
10

The vertex of a parabola is (-1.5, -12.5), and its y-intercept is (0, -8).

Mathematics
2 answers:
Pie3 years ago
8 0

Answer:

The x-intercept are x=-4,1.                    

Step-by-step explanation:

Given : The vertex of a parabola is (-1.5, -12.5), and its y-intercept is (0, -8).

To find : The x-intercepts of the parabola are ?

Solution :

The general form of the parabola equation is  

y=a(x-h)^2+k ......(1)

where, a is the initial value and (h,k) are vertex of the parabola.

We have given the vertex (h,k)=(-1.5, -12.5)

Substitute in equation (1),

y=a(x-(-1.5))^2+(-12.5)

y=a(x+1.5)^2-12.5 ......(2)

Now, The y-intercept is (0,-8)

Substitute in equation (2),

-8=a(0+1.5)^2-12.5

-8+12.5=a(1.5)^2

4.5=2.25a

a=\frac{4.5}{2.25}

a=2

Put back in equation (2),

y=2(x+1.5)^2-12.5

To find the x-intercept put y=0 in above equation,

0=2(x+1.5)^2-12.5

0=2(x^2+3x+2.25)-12.5

0=2x^2+6x+4.5-12.5

0=2x^2+6x-8

x^2+3x-4=0

Solve by middle term split,

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

x(x+4)-1(x+4)=0

(x+4)(x-1)=0

x+4=0,x-1=0

x=-4,1

Therefore, The x-intercept are x=-4,1.

Alecsey [184]3 years ago
4 0
The general equation of a parabola is y=ax^2+bx+c  At the y-intercept, x=0 and y= -8:  -8 = a(0)^2 + b(0) + c.  Thus, c = -8.  So, our equation becomes

y = ax^2 + bx - 8.  Next, substitute -1.5 for x and -12.5 for y.  Then,
-12.5 = a(-1.5)^2 + b(-1.5) - 8.  This simplifies to -4.5 = a(2.25) - 1.5b.

Next, take advantage of the info that the vertex is at x= -1.5.
The formula for the vertex is x=-b/(2a).    Letting this formula = -1.5, 

-1.5 = -b/(2a).  We can then solve for b:  1.5 = b/(2a), or 3a = b.

Now go back to the equation we derived previously:  -4.5 = a(2.25) - 1.5b.
Substitute 3a for b:

-4.5 = a(2.25) - 1.5(3a).    Then -4.5 = -2.25a, and a = 4.5/2.25 = 2.

Last, substitute a = 2 into   3a=b to determine the value of b.

b=3(2) = 6.

Therefore, your equation is y=2x^2 + 6x - 8.

Check this result.  Substitute the coordinates of the vertex (-1.5,-12.5) into this equation.  Is the equation still true?  If so, your equation correctly represents this parabola.
You might be interested in
Which inequality sign makes the statement true ?
masha68 [24]
Your answer is the last one!
6 0
2 years ago
Adrienne answered all 21 multiple choice questions correctly on her science test, if her teacher decides to let one of the quest
prisoha [69]
Since there are 21 questions and one is extra credit, the fraction is 21/20. Divide it to get 1.05. In percent, this is 105%. Hope this helps!
6 0
3 years ago
What is 2^4 divided by (4/10 times 2)
hichkok12 [17]

Answer:

20

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What value of w that makes the equation true 2/3(w+3) = 7
alexdok [17]
The answer is 7.5 or 15/2
3 0
3 years ago
What is the area of the polygon below
kvasek [131]
The area is 84.

What I do it cut the polygon into something easier like a square and rectangle.

Rectangle: 6•12=72
Square: 4•3=12

Add them together and you have 84
5 0
3 years ago
Other questions:
  • The population of fish in a certain lake follows the logistic growth function , where t is the time in years.
    12·1 answer
  • (05.03 LC)
    8·1 answer
  • Please help solve n - 425 = - 9<br> n = ______
    13·1 answer
  • Write the equation of a circle with a center at (2.5, –3.5) and a diameter of 12.
    13·1 answer
  • Answers?????????????
    15·2 answers
  • Can anyone help me do this
    9·1 answer
  • If (x+iy)³ = y+vi then show that (y/x + v/y) = 4(x²-y²)​
    5·2 answers
  • Can Someone Help Me With This Please
    7·1 answer
  • 2. √2x-5-√x+6=0(solving the following radical equations and check for extraneous solutions)
    15·1 answer
  • Dan makes $72 working 8<br> hours. How much does he<br> make per hour?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!