Question

Using the inverse matrix method, find the equation of the quadratic y=ax² +bx+c that contains the points (4, 8), (0, 12), and (7, -16). What is the equation?

A) y= (3/77)x²-(2/77)x+12
B) y= (2/77)x²-(3/77)x+12
C) y= (3/77)x²-(2/77)x+12
D) y= (2/77)x²-(3/77)x+12

Answer 1

The equation of the quadratic y=ax² +bx+c that contains the given points can be found using the inverse matrix method. The equation is y = (3/77)x² - (2/77)x + 12.

Step-by-step explanation:

The equation of the quadratic y=ax² +bx+c can be found using the inverse matrix method. We can set up a system of equations using the given points (4, 8), (0, 12), and (7, -16). Let's substitute the x and y values into the equation:

8 = 16a + 4b + c

12 = c

-16 = 49a + 7b + c

Since we have three equations and three variables (a, b, and c), we can use inverse matrices to solve for a, b, and c. Solving the system of equations, we find a = 3/77, b = -2/77, and c = 12.

Therefore, the equation of the quadratic is y = (3/77)x² - (2/77)x + 12.