Question

Write a quadratic function in standard form that represents the table below: BUNCH OF POINTS IF YOU HELP!

Answer 1

Explanation:

ax² + bx + c = y

( 0 , 3 ) ⇒ c = 3

( 1 , - 3 )

a(1)² + b(1) + 3 = - 3 ⇒ a + b = - 6 ⇒ a = - b - 6 ........ (1)

( 2 , - 5 )

a(2)² + b(2) + 3 = - 5 ⇒ 4a + 2b + 3 = - 5 ......... (2)

(1) -----> (2)

4( - b - 6 ) + 2b = - 8 ⇒ b = - 8

a = 2

y = 2x² - 8x + 3

Answer 2

To write a quadratic function in standard form, we need to find a, b, and c for the equation y = ax^2 + bx + c. We can use the given data points to create a system of equations to solve for a, b, and c.

Using the given points:

(-1, 13): 13 = a(-1)^2 + b(-1) + c
(0, 3): 3 = a(0)^2 + b(0) + c
(1, -3): -3 = a(1)^2 + b(1) + c

Now, we have a system of equations:

1. 13 = a - b + c
2. 3 = c
3. -3 = a + b + c
Substitute equation (2) into equations (1) and (3) to eliminate c:

1. 13 = a - b + 3
2. -3 = a + b + 3
Simplify:

1. 10 = a - b
2. -6 = a + b
Now, add equations (1) and (3) to eliminate b and solve for a:

(1) + (3): 4 = 2a
a = 2

Now that we have a, we can find b:

10 = 2 - b
b = -8

Now that we have a and b, we can substitute them back into equation (2) to find the quadratic function in standard form:

y = 2x^2 - 8x + 3