What is the equation, in standard form, of a parabola that contains the following points? ( -2, -23.5)(0,-4.5)(4,-26.5)

Skip to content# What is the equation, in standard form, of a parabola that contains the following points? ( -2, -23.5)(0,-4.5)(4,-26.5)

##
This Post Has 10 Comments

### Leave a Reply

What is the equation, in standard form, of a parabola that contains the following points? ( -2, -23.5)(0,-4.5)(4,-26.5)

D

Step-by-step explanation:

the the 5 minus the 12 and the 0 minus the negative one all finds it way. back to the equation d

-20 = 4a - 2b + c

-4 = c

-20 = 16a + 4b + c

4a - 2b + c = 16a + 4b + c

4a - 2b = 16a + 4b

-6b = 12a

b = -2a

-20 = 4a - 2b + c

-20 = 4a + 4a - 4

-16 = 8a

-2 = a

b = 4

c = -4

y = -2x^2 + 4x - 4

y = -2 * (x^2 - 2x) - 4

y = -2 * (x^2 - 2x + 1 - 1) - 4

y = -2 * (x^2 - 2x + 1) + 2 - 4

y = -2 * (x + 1)^2 - 2

Y = -2.5x^2 + 4.5^x + -4.5

[tex]What is the equation, in standard form, of a parabola that contains the following points? ( -2, -23[/tex]

y = -2*3x - 1

Step-by-step explanation:

The first term is -2 and the common ratio is 3 because every term is being multiplied by 3. The equation is y = -2*3x - 1.

The equation of parabola is [tex]y=-\frac{5}{2}x^2+\frac{9}{2}x-4.5[/tex].

Step-by-step explanation:

Equation of a parabola is quadratic equation.

Let the equation of parabola be

[tex]y=Ax^2+Bx+C[/tex] .... (1)

The parabola contains points ( -2, -23.5), (0,-4.5), (4,-26.5).

Put (0,-4.5) in equation (1),

[tex]-4.5=A(0)^2+B(0)+C[/tex]

[tex]-4.5=C[/tex]

Put this value in equation (1).

[tex]y=Ax^2+Bx-4.5[/tex] ... (2)

Put ( -2, -23.5) and (4,-26.5) in equation (2).

[tex]-23.5=A(-2)^2+B(-2)-4.5[/tex]

[tex]-19=4A-2B[/tex] .... (3)

[tex]-26.5=A(4)^2+B(4)-4.5[/tex]

[tex]-22=16A+4B[/tex] .... (4)

On solving (3) and (4), we get

[tex]A=-\frac{5}{2}[/tex] and [tex]B=\frac{9}{2}[/tex]

Therefore the value of parabola is

[tex]y=-\frac{5}{2}x^2+\frac{9}{2}x-4.5[/tex]

[tex]What is the equation, in standard form, of a parabola that contains the following points? ( -2, -23[/tex]

I believe your answer is C) y = -2x^2 + 4x - 4

C) y=x^2-2x+6

Step-by-step explanation:

We are given three points

(1,5) (-1,9) and (4,14)

We can verify each options

option-A:

[tex]y=x^2+6x+2[/tex]

we will verify each points

At (1,5):

we can plug x=1 and check whether y=5

[tex]y=(1)^2+6(1)+2[/tex]

[tex]y=9[/tex]

It does not satisfy point

So, this is FALSE

option-B:

[tex]y=x^2+6x-2[/tex]

we will verify each points

At (1,5):

we can plug x=1 and check whether y=5

[tex]y=(1)^2+6(1)-2[/tex]

[tex]y=5[/tex]

It satisfies point

At (-1,9):

we can plug x=-1 and check whether y=9

[tex]y=(-1)^2+6(-1)-2[/tex]

[tex]y=-7[/tex]

It does not satisfy point

So, this is FALSE

option-C:

[tex]y=x^2-2x+6[/tex]

we will verify each points

At (1,5):

we can plug x=1 and check whether y=5

[tex]y=(1)^2-2(1)+6[/tex]

[tex]y=5[/tex]

It satisfies point

At (-1,9):

we can plug x=-1 and check whether y=9

[tex]y=(-1)^2-2(-1)+6[/tex]

[tex]y=9[/tex]

So, it satisfies point

At (4,14):

we can plug x=4 and check whether y=14

[tex]y=(4)^2-2(4)+6[/tex]

[tex]y=14[/tex]

So, it satisfies point

so, this is TRUE

C) y = -2x^2 +4x - 4

Step-by-step explanation:

The y-values are the same for points (-2, -20) and (4, -20), so the axis of symmetry is halfway between those points, at x = (-2+4)/2 = 1.

The y-intercept is (0, -4), so the only viable answer choices are B and C. The axis of symmetry is given by ...

x = -b/(2a)

For choice B, this is x = -4/(2(-1)) = 2 (doesn't work).

For choice C, this is x = -4/(2(-2)) = 1, which matches the above analysis.

The appropriate choice is ...

y = -2x^2 +4x - 4

_____

Alternate solution

If you like, you can derive the equation for the parabola. Since you know that the y-intercept is -4, you can write the equation as ...

y = ax² +bx -4

Filling in the data points that are not x=0, we have two equations in two unknowns:

-20 = a(-2)² +b(-2) -4 ⇒ 4a -2b = -16

-20 = a(4)² + b(4) -4 ⇒ 16a +4b = -16

Adding twice the first equation to the second gives ...

2(4a -2b) + (16a +4b) = 2(-16) +(-16)

24a = -48

a = -2 . . . . . . . . matches choice C

4(-2) -2b = -16 . . . . . substitute into an equation to find b

-2b = -8 . . . . . . . . . . add 8

b = 4 . . . . . . . . . . . . . divide by -2

The equation that fits the given data is ...

y = -2x² +4x -4

[tex]What is the equation, in standard form, of a parabola that contains the following points? (-2, -20)[/tex]

answer:

15

step-by-step explanation:

f(x) = x² -3x +2

Step-by-step explanation:

We know from the first point that (x -2) is a factor of the polynomial, so we can write the other factor as (ax+b). Filling in the values from the other two given points, we have ...

f(x) = (x -2)(ax +b)

f(3) = (3 -2)(3a +b) = 2

f(4) = (4 -2)(4a +b) = 6

__

From the first of these, ...

3a + b = 2

Dividing the second by 2, we have ...

4a + b = 3

Subtracting the first of these equations from the second gives ...

(4a +b) -(3a +b) = (3) -(2)

a = 1

Using this in the first of the above equations, we have ...

3·1 + b = 2

b = -1

Then the factored form of the equation is ...

f(x) = (x -2)(x -1)

Expanding this to standard form, we have ...

f(x) = x² -3x +2

[tex]What is the equation, in standard form, of a parabola that contains the following points? (2,0), (3[/tex]