Question

Determine the equation of the quadratic relation in vertex form given the vertex (-3, -4) and that passes through (-5, 8). BRAINLIEST IF RIGHT ANSWER

Answer 1

Answer:

Step-by-step explanation:

If vertex has coordinates (- 3, - 4), then axis of symmetry is x = - 3.

Point (- 1, 8) is reflection of point (- 5, 8) across x = - 3 and lays on parabola.

Assume the equation of the parabola is ax² + bx + c = y .

Since the parabola passes through the point (- 3, - 4) , then

- 4 = 9a - 3b + c

Since the parabola passes through the point (- 5, 8), then

8 = 25a - 5b + c

Since the parabola passes through the point (-1, 8), then

8 = a - b + c

Thus, we have to obtain the following system of equations

9a - 3b + c = - 4

25a - 5b + c = 8

a - b + c = 8

Solving the system (see attachment), we get the

a = 3 , b = 18, c = 23

Thus, the standard form of the equation of the parabola is

y = 3x² + 18x + 23

Vertex form of quadratic equation is y = a(x - h)² + k , where (h, k) vertex of the parabola.

Thus, the vertex form of the quadratic relation is

y = 3(x + 3)² - 4

Answer 2

Step-by-step explanation:

Given Determine the equation of the quadratic relation in vertex form given the vertex (-3, -4) and that passes through (-5, 8)  

• In the vertex form, the quadratic equation is written as
• So f(x) = a(x – h)^2 + k
• Where (h,k) is the vertex and a is a constant.
• So given (h,k) = (-3,-4)
• Therefore we can write it as
• So f(x) = x(x + 3)^2 – 4
• Now the equation passes through the point (-5,8)
• So 8 = a(-5 + 3)^2 – 4
• 8 = a(- 2)^2 – 4
• 8 = 4a – 4
• 4a = 12
• Or a = 3
• Now in the vertex form the quadratic equation can be written as
• So f(x) = 3(x + 3)^2 – 4
•           = 3(x^2 + 6x + 9 ) – 4
•          = 3x^2 + 18 x + 27 – 4
•         = 3x^2 + 18x + 23

Reference link will be

https://brainly.in/question/9305986