Question

Find a value of c so that y = x^2 - 12x + c has exactly one zero. A zero is an x-intercept. Find an equation with one x-intercept.

Answer 1

c=36

`y = x^2 - 12x + 36`

Explanation:

Given the equation
`y = x^2 - 12x + c`

We are to determine the value of c for which y has only one zero.

For the general form of a quadratic equation
`ax^2+bx+c=0`, we can use the Discriminant to determine the nature of the roots.

If the Discriminant,
`D=b^2-4ac=0`, then the equation has equal roots, i.e. one x-intercept.

`y = x^2 - 12x + c\\a=1, b=-12, c=c\\D=(-12)^2-(4*1*c)=0\\144-4c=0\\-4c=-144\\c=36`

When c=36, the equation has only one root.

The equation therefore is:
`y = x^2 - 12x + 36`