Question

Determine an equation of a Quadratic function

Answer 1

Answer:

y = -4x² + 32x - 48

Step-by-step explanation:

The standard form of a quadratic equation is  

y = ax² + bx + c

We must find the equation that passes through the points:

(2, 0), (6,0), and (3, 12)

We can substitute these values and get three equations in three unknowns.

0 = a(2²) + b(2) + c

0 = a(6²) + b(6) + c

12 = a(3²) + b(3) + c

We can simplify these to get the system of equations:

(1)   0 =    4a + 2b + c

(2)  0 = 36a + 6b + c

(3) 12 =   9a + 3b + c

Eliminate c from equations (1) and (2). Subtract (1) from (2).

(4) 0 = 32a + 4b

Eliminate c from equations (2) and (3). Subtract (3) from (2).

(5) -12 = 27a - 3b

Simplify equations (4) and (5).

(6)  0 = 8a + b

(7) -4 = 9a  - b

Eliminate b by adding equations (6) and (7).

(8) a = -4

Substitute (4) into (6).

    0 = -32 + b

(9) b =  32

Substitute a and b into (1)

0 = 4(-4) + 2(32) + c

0 = -16 + 64 + c

0 = 48 + c

c = -48

The coefficients are

a= -4, b = 32, c = -48

The quadratic equation is

y = -4x² + 32x - 48

The diagram below shows the graph of your quadratic equation and the three points through which it passes.