Question

Use y = 3x2 + 18x - 2 to answer the following question(1, 19) is a point on the graph. What point is the reflection of (1, 19) across the axis of symmetry of the parabola?

Answer 1

Since y is a parabolla, there will be two values for y = 19. We already know that x = 1 is one value, to find the other, we can substitute y = 19 on the equation and solve for x to get the following:

`\begin{gathered} 19=3x^2+18x-2 \\ \Rightarrow3x^2+18x-2-19=0 \\ \Rightarrow3x^2+18x-21=0 \\ \Rightarrow3(x^2+6x-7)=0 \\ \Rightarrow3(x-1)(x+7)=0 \end{gathered}`

the solutions of the equation are x = 1 and x = -7. Since we already have that (1,19) is a point on the graph, then we have that the other point is (-7,19)