find an equation of quadratic function the graph passes through the points A(2,3)B(-1,0) and C (1,0)

Answer 1

To find the quadratic function that passes through these three points, we can use the general form of a quadratic function:

f(x) = ax^2 + bx + c

where a, b, and c are unknown constants that we need to find. To do this, we can plug in the coordinates of each point and get a system of three equations:

f(2) = 4a + 2b + c = 3
f(-1) = a - b + c = 0
f(1) = a + b + c = 0

We can solve this system of equations by eliminating one of the unknowns, say c. For example, we can add the second and third equations to get:

2a = 0

which implies that a = 0. Substituting this into the other two equations, we can solve for b and c:

b = 3/2
c = -3/4

Therefore, the quadratic function is:

f(x) = (3/2)x - 3/4

or

f(x) = 1.5x - 0.75 (in decimal form)