Question

Which equation represents a graph with a vertex at (1, -6)?

y=3x^2+6x-3
y=3x^2-6x-3
y=3x^2-8x-1
y=3x^2-3x-6

Answer 1

`\textsf{B)} \quad y=3x^2-6x-3`

Explanation:

`\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is the leading coefficient.\\\end{minipage}}`

If the vertex is (1, -6) then h = 1 and k = -6:

`\implies y=a(x-1)^2+(-6)`

`\implies y=a(x-1)^2-6`

From inspection of the answer options, the leading coefficient is 3.

Therefore, a = 3:

`\implies y=3(x-1)^2-6`

Expand the equation to standard form:

`\implies y=3(x^2-2x+1)-6`

`\implies y=3x^2-6x+3-6`

`\implies y=3x^2-6x-3`