Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Answer:
- y = -3x² + 7x - 9
Step-by-step explanation:
Given quadratic function:
- y = ax² + bx + c
Points on the graph:
- (-2,-35), (1,-5), (3,- 15)
Substitute values of x and y and solve the system of equations:
- -35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c ⇔ eq 1
- -5 = a(1)² + b(1) + c ⇒ -5 = a + b + c ⇔ eq 2
- -15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c ⇔ eq 3
Subtract eq 2 from eq 1:
- -35 - (-5) = 4a - 2b + c - a - b - c
- -30 = 3a - 3b
- b = a + 10 ⇔ eq 4
Subtract eq 2 from eq 3:
- -15 - (-5) = 9a + 3b + c - a - b - c
- -10 = 8a + 2b
- b = -4a - 5 ⇔ eq 5
Compare eq 4 and eq 5, solve for a:
- a + 10 = -4a - 5
- a + 4a = -5 - 10
- 5a = -15
- a = -3
Find the value of b using eq 4:
- b = -3 + 10
- b = 7
Find the value of c using eq 2:
- -5 = -3 + 7 + c
- c = -5 - 4
- c = -9
We now have a, b and c:, the function is:
- y = -3x² + 7x - 9
Answer:
y = -3x² + 7x - 9
Step-by-step explanation:
Given quadratic function:
y = ax² + bx + c
Points on the graph:
(-2,-35), (1,-5), (3,- 15)
Substitute values of x and y and solve the system of equations:
-35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c ⇔ eq 1
-5 = a(1)² + b(1) + c ⇒ -5 = a + b + c ⇔ eq 2
-15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c ⇔ eq 3
Subtract eq 2 from eq 1:
-35 - (-5) = 4a - 2b + c - a - b - c
-30 = 3a - 3b
b = a + 10 ⇔ eq 4
Subtract eq 2 from eq 3:
-15 - (-5) = 9a + 3b + c - a - b - c
-10 = 8a + 2b
b = -4a - 5 ⇔ eq 5
Compare eq 4 and eq 5, solve for a:
a + 10 = -4a - 5
a + 4a = -5 - 10
5a = -15
a = -3
Find the value of b using eq 4:
b = -3 + 10
b = 7
Find the value of c using eq 2:
-5 = -3 + 7 + c
c = -5 - 4
c = -9
We now have a, b and c:, the function is:
y = -3x² + 7x - 9
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
