Find, in the form , the equation of the quadratic whose…

MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials

Problem

Find, in the form

y=ax^2+bx+c

, the equation of the quadratic whose graph: (1) cuts the

x

-axis at

5

and

1

, and passes through

(2,-9)

(2) cuts the

x

-axis at

2

and

-\dfrac{1}{2}

, and passes through

(3,-14)

(3) touches the

x

-axis at

3

and passes through

(-2,-25)

(4) touches the

x

-axis at

-2

and passes through

(-1,4)

(5) cuts the

x

-axis at

3

, passes through

(5,12)

, and has axis of symmetry

x=2

(6) cuts the

x

-axis at

5

, passes through

(2,5)

, and has axis of symmetry

x=1