Video Transcript
Which of the following equivalent forms of the equation graphed in the given 𝑥𝑦-plane shows the coordinates of vertex 𝐵 as constants in the equation? A) 𝑦 equals two times 𝑥 minus one times 𝑥 minus five. B) 𝑦 equals two times 𝑥 squared minus six 𝑥 plus 10. C) 𝑦 equals two times 𝑥 squared minus six 𝑥 plus five. Or D) 𝑦 equals two times 𝑥 minus three squared minus eight.
There are a few things we should note about this question. The first is that we’re given equivalent forms of the equation. And that means if you plugged all four of these equations into the calculator, they would graph the same line. And so we’re looking for something else. We’re looking for a form of the equation that gives the coordinates of a vertex. here the vertex is 𝐵. And it’s located at three along the 𝑥-axis and negative eight along the 𝑦-axis. The coordinate form of vertex 𝐵 would be three negative eight.
And we want to know in which of these four equivalent forms do these coordinates show up as constants. Only one of the equations has three and negative eight as constants. And that’s option D. Option D is a form of an equation that we call the vertex form. The vertex form is the form 𝑦 equals 𝑎 times 𝑥 minus ℎ squared plus 𝑘 where ℎ, 𝑘 is the vertex. Looking at this form, we can tell that the vertex of this equation will be located at three, negative eight.
