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
Rashid [163]
3 years ago
15

What is the equation in standard form of a parabola that models the values in the table

Mathematics
2 answers:
Damm [24]3 years ago
5 0
To solve this, you can do it the easy way or hard way

easy way is to know some stuff about parabolas and zeroes

hard way is to subsitute for x and f(x) and solve for a,b, and c with a system of 3 variables (harder)



I'm going to do the easy way
nice we are given some zeroes

when f(x)=0, x=-2
since it is quadratic, it is 2nd degree and we can write all 2nd degree functions in the form f(x)=a(x-b)(x-c)
where a is some random constant and b and c are the x intercepts
we are given that when f(x)=0, x=-2, that means one x intercept is at -2
so lets say b=-2
f(x)=a(x-(-2))(x-c)
f(x)=a(x+2)(x-c)
great, now to find the other values
when x=0, y=-6
subsitute 0 for x and see what happens
-6=a(0+2)(0-c)
-6=a(2)(-c)
-6=-2ac
divide by -2 both sides
3=ac
cool
we revisit our equation
f(x)=a(x+2)(x-c)
now if we solve for a, we can do
3=ac, a=3/c, subsitute 3/c for a
f(x)=(3/c)(x+2)(x-c)
subsitute (4,78)
78=(3/c)(4+2)(4-c)
78=(3/c)(6)(4-c)
divide both sides by 6 for ease
13=(3/c)(4-c)
13=12/c-3
add 3 to both sides
16=12/c
multiply both sides by c
16c=12
divide both sides by 16
c=12/16
c=0.75
find a
a=3/c
a=3/0.75
a=4
if might be best to leave in fraction form
a=4
c=0.75=3/4

the equation is
f(x)=4(x+2)(x-\frac{3}{4})
in standard form as in ax^2+bx+c form
f(x)=4x^2+5x-6
Pachacha [2.7K]3 years ago
5 0

Answer:

f(x) = 4x^2 + 5x -6

Step-by-step explanation:

We are given with table of values

Standard form of parabola equation is

f(x)=ax^2 +bx+c

Plug in the values given in the table and  make three equations

Then solve for a,b,c

x=-2 , f(x) = 0

So equation becomes 0= a(-2)^2+b(-2)+c

4 a - 2 b + c=0 --------> equation 1

x=0 , f(x) = -6

So equation becomes -6= a(0)^2+b(0)+c

c= -6

x=4 , f(x) = 78

So equation becomes 78= a(4)^2+b(4)+c

16 a + 4 b + c=78--------> equation 2

We got c=-6, plug in -6 in both equations 1  and 2

4 a - 2 b - c =0--------> equation 1

4a - 2 b = 6 --------------> equation 3

16 a + 4 b + c=78--------> equation 2

16 a + 4 b = 78+6

16 a + 4 b = 84 ------------> equation 4

Multiply the third equation by 2

4a - 2 b = 6 --------------> equation 3

8a - 4b = 12

16 a + 4 b = 84 ------------> equation 4 (add the  above equation)

------------------------------------

24a = 96

Divide both sides by 24

so a= 4

Now plug in 4 for 'a' in equation 3

4a - 2 b = 6

4(4) -2b= 6

16 - 2b = 6

subtract 16 on both sides

-2b = -10

Divide both sides by -2

So b= 5

Hence a= 4, b=5  and c= -6

Standard form of parabola equation is

f(x)=ax^2 +bx+c

f(x) = 4x^2 + 5x -6



You might be interested in
How do I determine which is y=-1/3x+2?
Jlenok [28]

Step-by-step explanation:

This is a linear equation in slope intercept form which is

y = mx + b

where m is the slope and b is the y intercept.

The equation

y =  -  \frac{1}{3} x + 2

Has a slope of -1/3 so this means that the slope will be decreasing. A negative linear equation increases as we go left. and decreases as we go right. The y intercept is 2. So this means the graph must pass through (0,2) and when x=0, y must be 2.

In other words, look for a line that the y values increase as we go left and decrease we go right. Also look for a point (0,2) and make sure the graph pass through it.

6 0
3 years ago
Is -4 less than or greater than -6?
Aleks [24]

Answer:

-4 is greater then -6

Step-by-step explanation:

-4 is closer to 0

3 0
2 years ago
Read 2 more answers
Help me Solve 1/6 ÷ 2/6 please
pochemuha
\frac{1}{6} ÷ \frac{2}{6}

First, apply this following rule: a ÷ \frac{b}{x} = a × \frac{c}{b}
\frac{1}{6} × \frac{6}{2}
Second, apply this following rule: \frac{a}{b} × \frac{c}{d} =  \frac{ac}{bd}
\frac{1x6}{6x2}
Third, multiply 1 × 6 to get 6 and 6 × 2 to get 12.
\frac{6}{12}
Fourth, find the GCF of 6 and 12. 
Factors of 6: 1, 2, 3, 6
Factors of 12: 1, 2, 3, 4, 6, 12
The GCF is 6.
Fifth, divide the numerator by the GCF.
6 ÷ 6 = 1
Sixth, divide the denominator by the GCF.
12 ÷ 6 = 2
Seventh, collect the new numerator and new denominator.
\frac{1}{2}

Answer as fraction: \frac{1}{2}
Answer as decimal: 0.5

8 0
3 years ago
Convert 7/8 to a decimal Then determine if the decimal is terminating or repeating
Black_prince [1.1K]

Answer:

0.875 = 7/8 and it is terminating

Step-by-step explanation:

4 0
3 years ago
Graph the line with slope 1/2 passing through the point (5, - 1)
True [87]

Answer:

<u><em>The equation is y = (1/2)x + - 3.5</em></u>

Step-by-step explanation:

We look for an equation with the form y = mx + b, where m is the slope and b the y-intercept.

We're given the slope, (1/2) which we can use for m:

y = (1/2)x + b

We are told the line goes through (5,-1).  We need a value of b that will move the line to include this point.  Do that by substituting the values:

 x = 5, and y= -1

y = (1/2)x + b

-1 = (1/2)*5 + b

-1 = (2.5) + b

- 3.5 =   b

<u><em>The equation is y = (1/2)x + - 3.5</em></u>

See the attached image.

7 0
10 months ago
Other questions:
  • How to solve (8.76 x 109)(6.52 x 10-3)/13.27 x 105?
    12·1 answer
  • Solve these equations. |x+8|=x+8
    13·1 answer
  • PLEASE HELP!!! How many solutions does each polynomial have?​
    5·1 answer
  • At a deli, 56 sandwiches were sold during lunchtime. Twenty-five percent of the sandwiches sold were tuna salad. How many of the
    11·1 answer
  • Preform the indicated operation. (w^3+64) divided (4+w)
    10·1 answer
  • What number is 5 10's greater than 89?
    9·1 answer
  • Sin (x)= 0.78 what is x?
    10·2 answers
  • Suppose you have $245. If you decide to spend it all on ice cream, you can buy 70 pints. If the price of a glass of lemonade is
    10·1 answer
  • <img src="https://tex.z-dn.net/?f=%5Csqrt%7B25%7D" id="TexFormula1" title="\sqrt{25}" alt="\sqrt{25}" align="absmiddle" class="l
    15·2 answers
  • Question:
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!