Question

Find a quadratic function that includes the set of values below.

(0,9), (2,19), (4,13)

The equation of the parabola is y =_______

Answer 1

y = -2x^2 + 9x + 9

Explanation:

y = ax^2 + bx + c

Now, plug in each point to create a system of three equations:

1. For (0,9): 9 = a(0)^2 + b(0) + c, which simplifies to c = 9.

2. For (2,19): 19 = a(2)^2 + b(2) + 9, which simplifies to 4a + 2b = 10.

3. For (4,13): 13 = a(4)^2 + b(4) + 9, which simplifies to 16a + 4b = 4.

Now, solve this system of equations to find the values of 'a' and 'b':

From equation 2: 4a + 2b = 10

From equation 3: 16a + 4b = 4

You can start by multiplying equation 2 by -4 to eliminate 'b':

-16a - 8b = -40

Now, add this to equation 3:

16a + 4b - 16a - 8b = 4 - 40

This simplifies to:

-4b = -36

Divide both sides by -4:

b = 9

Now that you have 'b,' you can substitute it into equation 2:

4a + 2(9) = 10

4a + 18 = 10

Subtract 18 from both sides:

4a = -8

Divide both sides by 4:

a = -2

So, the equation of the quadratic function is:

y = -2x^2 + 9x + 9