Mathematico | Mathematico

The vertex of the parabola

y = x^{2} + 6 x + c

lies on the parabola

y = x^{2}

Find the value of $c$ .

Hint

In complete square form, we have

y = (x + 3)^{2} - 9 + c

Hint

So the vertex is at the point

(- 3, c - 9)

We are told that these coordinates satisfy $y = x^{2}$

Solution

In complete square form, we have

y = (x + 3)^{2} - 9 + c

so the vertex is at the point

(- 3, c - 9)

We are told that these coordinates satisfy $y = x^{2}$ , therefore

\begin{aligned} c - 9 & = (- 3)^{2} \\ c & = 18 \end{aligned}