Write the quadratic function in standard form fx x2 6x 1...

Write the quadratic function in standard form. f(x) = x^2 - 6x + 1 Sketch its graph. Identify the vertex, axis of symmetry, and x-intercept(s). (If an answer does not exist, enter DNE.)

Transcript

00:01 So in this problem, what you're being asked to do is to write the original equation or the function here in standard form.

00:07 Well, this quadratic is actually already in standard form because it goes our x squared term, our x term, and our constant.

00:13 So it is actually already in standard form.

00:15 So what we want to do is make a sketch for this function.

00:18 So let's set up a coordinate plane here.

00:23 4, 5, 6.

00:24 I'll just go in 6 direction to start with and we'll see if we need more than that in a second.

00:28 So here's our y -axis.

00:32 And our x -axis.

00:34 Okay.

00:34 Well, in order to graph this, the first thing we need to do is find the vertex.

00:38 Well, to find the vertex, we have a formula.

00:40 It's x equals negative b over 2a, where b is the coefficient of our x term, so that'll be negative 6, and a is the coefficient of our x -square term, which remember, if you don't see it, it's an imagine every 1.

00:53 So we have 2 times 1.

00:55 Well, minus negative 6 is positive 6, 2 times 1 is 2, and 6 divided by 2 is 3.

01:01 So the x -quering of our vertex happens when x is 3.

01:04 Now we need to find the y value.

01:06 So to find the y value, that means we have to find f of 3.

01:09 So we're going to have 3 squared minus 6 times 3 plus 1.

01:13 Well, 3 squared is 9.

01:15 Negative 6 times 3 is negative 18 plus 1.

01:18 So we have 9 minus 18, which is negative 9, and negative 9 plus 1 is negative 8.

01:23 So now we know the ordered pair for our vertex is 3 -9.

01:26 So i am going to need a little bit more room down here.

01:29 7, 8, 9.