Question

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

(0,6), (2,16), (4,10)
The equation of the parabola is y = _
A) y = -2x² + 12x + 6
B) y = 2x² + 2x + 6
C) y = -2x² + 20x + 6
D) y = -x² + 8x + 6

Answer 1

Option A). The equation of the quadratic function that includes the given set of values is y = -2x^2 + 12x + 6.

Step-by-step explanation:

The equation of the quadratic function that includes the given set of values can be found using the method of substitution.

Let's start by substituting the x and y values from one of the given points into the general form of a quadratic function: y = ax^2 + bx + c.

Using the point (0,6), we get:

6 = a(0)^2 + b(0) + c

6 = c. So, we now have c = 6.

Now, substitute the x and y values from another point, let's use (2,16):

16 = a(2)^2 + b(2) + 6

16 = 4a + 2b + 6

4a + 2b = 10

Finally, substitute the x and y values from the last point, (4,10):

10 = a(4)^2 + b(4) + 6

10 = 16a + 4b + 6

16a + 4b = 4

We now have a system of equations:

4a + 2b = 10

16a + 4b = 4

Solving this system of equations, we find a = -2 and b = 12.

Therefore, the equation of the quadratic function that includes the given set of values is y = -2x^2 + 12x + 6.