Question

what is the equation in standard form of a parabola that contains the following points (-2, -20), (0 ,-4),(4,-20)

Answer 1

Given :

What is the equation, in standard form, of a parabola that contains the following points:

(–2, 18), (0, 2), (4, 42)

ax^2 + bx + c = y - standard form, of a parabola equation
Solve for a b and c :

Step 1 :

Solve for c { this is a give me. you will see why in the below }


ax^2 + bx + c = y

a(0^2) + b(0) + c = 2 - plugging or replacing x with 0 and y with 2

since anything times zero is 0 so

0 + 0 + c = 2 - the above reasons

c = 2 - Addition

see I told you this was a give me

solve for a

ax^2 + bx + 2 = y - Plugging c with 2

a(-2^2 ) - 2b + 2 = 18 - plugging x and y with -2 and 18
a(4^2 ) + 4b + 2 = 42 - plugging x and y with 4 and 42

4a - 2b + 2 = 18
16a + 4b + 2 = 42 - Solving the squares of - 2 and 4

Need a common value to remove the b by multiplication and solve for a though the addition of terms
4 is good so I will use it

(2) 4a - 2b + 2 = 18( 2)
16a + 4b + 2 = 42 - multiplying 2 to one of the equation to remove the b's from it by the addition of terms


8a - 4b + 4 = 36
16a + 4b + 2 = 42
--------------------------- - Multiplication and the addition of terms
24a + 6 = 78


24a + 6 = 78 - -derived equation from the above

24a + 6 - 6 = 78 + - 6 -Adding a -6 to both sides of the equation to remove 6 from one side of it and put - 6 on the other side

24a = 72 - Addition

1/24 * 24a = 72 * 1/24 - timing both sides of the equation with 1/24 to solve for a

a = 72/24 - multiplication

a = 3 - division

Let solve for b

4a - 2b + 2 = 18 - one of the equation from the above

4(3) - 2b + 2 = 18 - plugging a with 3

12- 2b + 2 = 18 - multiplication of 4 and 3

14 - 2b = 18 - Addition of 12 and 2

-14 + 14 - 2b = 18 - 14 - -Adding a -14 to both sides of the equation to remove 14 from one side of it and put - 14 on the other side

-2b = 4 - Addition

-1/2 * -2 b = 4 * -1/2 timing both sides of the equation with -1/2 to solve for b

b = -4/2 - multiplication

b = - 2 - Division

So

a = 3 , b = -2 , c = 2 or 3x^2 + -2x + 2 = y ===> your equation ( or Answer)

Proof or check :

ax^2 + bx + c = y

3x^2 + - 2 x + 2 = y - plugging a , b, c with 3,-2,2

3(-2^2) - 2 (-2) + 2 = 18 - plugging x and y with -2 and 18
3(0^2) -2( 0) + 2 = 2 - plugging x and y with 0 and 2
3(4^2) - 2 (4) + 2 = 42 - plugging x and y with 4 and 42


3(4) + 4 + 2 = 18
3(0) + 0 + 2 = 2
3(16) - 8 + 2 = 42 - solving the squares of -2,0,4 and multiplication

12 + 4 + 2 = 18
0 + 0 + 2 = 2
48 - 8 + 2 = 42 - multiplication

18 = 18
2 = 2
42 = 42 - Addition

It checks and equals

Answer 2

thanks

Answer 3

Welcome no problem