Question

Math homework.....please help??!?!!?!?

Answer 1

Observe the graphs, they are parabolas.

A quadratic function represents parabola in the graph.

General form of parabola is f(x) = ax² + bx + c

Quadratic function has two factors.

 

A)The parabola opens upward.

So the sign of a is positive.

x intercepts are  - 3, 2

So ( x + 3) and ( x - 2) are factors of f(x).

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

= x²  + 3x - 2x - 6

= x²  + x  - 6

Required equation is y = x²  + x  - 6.

Answer 2

B)The parabola opens downward.

So the sign of a is negative.

x intercepts are  - 3, 0

So ( x + 3) and  x are factors of f(x).

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

= - x²  - 3x

Required equation is y = - x²  - 3x .

 

C)The parabola opens upward.

So the sign of a is positive.

x intercepts are  1, 5

So ( x - 1) and ( x - 5) are factors of f(x).

f(x) = (x - 1)(x - 5)

= x²  - 5x - x + 5

= x²  - 6x  + 5

Required equation is y = x²  - 6x  + 5.