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

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

1. nakuhernandez says:

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

2. prin30004 says:

-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

3. buky0910p6db44 says:

Y = -2.5x^2 + 4.5^x + -4.5
$What is the equation, in standard form, of a parabola that contains the following points? ( -2, -23$

4. hinsri says:

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.

5. canyonrico05 says:

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

Step-by-step explanation:

Equation of a parabola is quadratic equation.

Let the equation of parabola be

$y=Ax^2+Bx+C$                  .... (1)

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

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

$-4.5=A(0)^2+B(0)+C$

$-4.5=C$

Put this value in equation (1).

$y=Ax^2+Bx-4.5$               ... (2)

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

$-23.5=A(-2)^2+B(-2)-4.5$

$-19=4A-2B$                     .... (3)

$-26.5=A(4)^2+B(4)-4.5$

$-22=16A+4B$                  .... (4)

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

$A=-\frac{5}{2}$ and $B=\frac{9}{2}$

Therefore the value of parabola is

$y=-\frac{5}{2}x^2+\frac{9}{2}x-4.5$

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

6. sarah7484 says:

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

7. juliangarcia0002 says:

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:

$y=x^2+6x+2$

we will verify each points

At (1,5):

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

$y=(1)^2+6(1)+2$

$y=9$

It does not satisfy point

So, this is FALSE

option-B:

$y=x^2+6x-2$

we will verify each points

At (1,5):

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

$y=(1)^2+6(1)-2$

$y=5$

It satisfies point

At (-1,9):

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

$y=(-1)^2+6(-1)-2$

$y=-7$

It does not satisfy point

So, this is FALSE

option-C:

$y=x^2-2x+6$

we will verify each points

At (1,5):

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

$y=(1)^2-2(1)+6$

$y=5$

It satisfies point

At (-1,9):

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

$y=(-1)^2-2(-1)+6$

$y=9$

So, it satisfies point

At (4,14):

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

$y=(4)^2-2(4)+6$

$y=14$

So, it satisfies point

so, this is TRUE

8. Treshard says:

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

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

9. BrodsterBj says:

15

step-by-step explanation:

10. shantejahtierr3754 says:

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

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