29.2k views
0 votes
What is the equation in standard form of a parabola that models the values in the table (-2,0),(0,-6),(4,78)

User Ziu
by
8.0k points

2 Answers

3 votes

Answer:

The equation is:

f(x) = 4x² + 5x -6

Step-by-step explanation:

A parabola is a second degree equation that has the general (standard) formula: f(x) = ax² + bx + c

Now, to get the equation of the parabola having points (-2,0) , (0,-6) and (4,78) we need to get the values of a, b and c.

1- Substitute with point (0, -6) in the general equation as follows:

f(x) = ax² + bx + c

-6 = a(0)² + b(0) + c

c = -6

Therefore, the equation of the parabola now becomes:

f(x) = ax² + bx - 6

2- Substitute with point (-2 , 0) in the equation we got from part 1:

f(x) = ax² + bx - 6

0 = a(-2)² + b(-2) - 6

0 = 4a - 2b - 6 ................> Divide all terms by 2

0 = 2a - b - 3

b = 2a - 3 ................> equation I

3- Substitute with point (4,78) in the equation we got from part 1:

f(x) = ax² + bx - 6

78 = a(4)² + b(4) - 6

78 = 16a + 4b - 6

78 + 6 = 16a + 4b

84 = 16a + 4b ................> equation II

Substitute with equation I in equation II and solve for a as follows:

84 = 16a + 4b

84 = 16a + 4(2a-3)

84 = 16a + 8a - 12

84 + 12 = 24a

96 = 24a

a = 4

Now, substitute with the value of a in equation I to get b as follows:

b = 2a - 3

b = 2(4) - 3 = 8 - 3 = 5

From the above calculations, we can conclude that:

The equation of the required parabola is:

f(x) = 4x² + 5x -6

Hope this helps :)

User Johannes Leimer
by
8.7k points
0 votes
hello here is a solution : 
What is the equation in standard form of a parabola that models the values in the-example-1
What is the equation in standard form of a parabola that models the values in the-example-2
User Zaplec
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories