quadratic functions

Question

write a quadratic function given the roots (3,0) and (-1,0) and the point (4,10)

Answer 1

A quadratic equation is an equation that has a parabolic shape.  The degree of this function is 2.

 

The roots are the values of x that make the function equal to zero.  Since we know our zeros and one additional point, we can set the equation as

 

f(x) = C(x - 3)(x + 1)

 

 

C is a constant.  To find this constant, we use the addition point and plug it into the function we have so far.

 

 

10 = C(4 - 3)(4 + 1)

10 = 5C

2 = C

 

 

Plug in this value of C into the function.

 

f(x) = 2(x - 3)(x + 1)

 

f(x) = 2(x² - 2x - 3)

 

f(x) = 2x² - 4x - 6

 

 

 

Answer 2

2x^2-4x-6