Mathematics

Problem

Find, in the form

y = ax^2 + bx + c

, the equation of the quadratic whose graph: a. cuts the

x

-axis at 5 and 1, and passes through $(2, -9) b. cuts the

x

-axis at 2 and

-\frac{1}{2}

, and passes through $(3, -14) c. touches the

x

-axis at 3 and passes through $(-2, -25) d. touches the

x

-axis at

-2

and passes through $(-1, 4) e. cuts the

x

-axis at 3, passes through

(5, 12)

, and has axis of symmetry $x = 2 f. cuts the

x

-axis at 5, passes through

(2, 5)

, and has axis of symmetry

x = 1