finding the vertex of a quadratic function

Going to hit a minimum point when this part of theĮxpression is equal to zero because this thing, the Realize, like, okay look, for this particular one, we're This is actually called vertex form because it's veryĮasy to pick out the vertex. And, when t is equal toįive, what is f of t? What is f of five? Well, when t is equal to five, five minus five squared is just zero. The t coordinate is five and five is three away from eightĪnd three away from two. It's going to be halfway in between where the parabola, in this case, is going to intersect the x axis, or the t axis, I keep saying x axis, the t axis for this case. Vertex is going to be halfway in between the zeros. T coordinate of the vertex since the input variable here is t, the t coordinate of the So, the x coordinate of the vertex, or sorry, I should say the T is equal to eight or two, the function is going to be zero. Have found the zeros for this function because if

And to solve for t, we couldĪdd five to both sides, so we get t is equal toĮight or t is equal to, if we add five to both sides here, t is equal to two. Is nine, that means that t minus five could be equal to the positive square root of nine or t minus five could equal the negative square root of nine. We add nine to both sides the lefthand side's just Minus nine, equal zero? Let's see, to solve this, weĬould add nine to both sides. So, to find the zeros, we can set t minus five squared, So, let's see, so let'sįirst find the zeros. And if, at any point, you get inspired pause the video again and And I'm assuming you just did that and now I am going to attempt to do it. See if you can figure out the zeros, the vertex,Īnd the line of symmetry. Which will actually be the only line of symmetry for these three. And in particular, to make itĪ little bit more specific, the vertical line of symmetry, And finally, I want to find the equation of the line of symmetry. I also want to find theĬoordinates of the vertex. Here, it'd be the x values that make the function equal zero. And so, the zeros are the input values that make the value of theįunction equal to zero.

I know they're all called f, but we're gonna just assume

Finding the vertex of a quadratic function