Determine the equation of the quadratic relation in vertex form given the vertex (-3, -4) and that passes through (-5, 8). Then put into standard form (y = ax 2 +bx + c). Determine the maximum or minimum value and state its value. QUICK MATH need help!
Answers
Answer:
Step-by-step explanation:
Assume that the equation of the parabola is
y = ax² + bx + c
Since the parabola passes through the point (- 5, 8), then
8 = 25a - 5b + c
Since the parabola passes through the point (- 3, - 4), then
- 4 = 9a - 3b + c
Since the parabola passes through the point (- 1, 8) which is reflection of the point (-5, 8) over axis of symmetry x = - 3, then
8 = a - b + c
9a - 3b + c = - 4
25a - 5b + c = 8
a - b + c = 8
Standard form is y = 3x² + 18x + 23
Vertex form is y = 3(x +3)² - 4
The minimum value is (- 4)
Given : quadratic relation in vertex form given the vertex (-3, -4) and that passes through (-5, 8).
To find : put into standard form
Solution:
y = ax² + bx + c
vertex (-3, -4)
=> -4 = 9a -3b + c
passes through (-5, 8).
=> 8 = 25a -5b + c
=> 12 = 16a - 2b
=> 8a - b = 6
vertex (-3, -4)
Hence (-3, -4) will be maxima or minima
as it passed through (-5 , 8)
Hence -4 is minima
(-3 , - 4) is minimum Value
so - 3 is Axis of symmetry
hence (-1 , 8) will also lies on curve
Hence
8 = a - b + c
25a -5b + c = a - b + c
=> 24a = 4b
=> b = 6a
8a - b = 6
=> 8a - 6a = 6
= > 2a = 6
=> a = 3
=> b = 18
8 = a - b + c
=> 8 = 3 - 18 + c
=> c = 23
y = 3x² + 18x + 23
dy/dx = 6x + 18
=> x = - 3
d²y/dx² = 6 > 0
Hence minimum value at x = - 3 which is - 4
y = 3x² + 18x + 23
minimum value
Learn more:
Vertex A (4, –5) and point of intersection O (–6, 7) of diagonals of ...
https://brainly.in/question/12195097
A point where two sides of triangle meet is known as - of a triangle ...
https://brainly.in/question/6135034