7. (1 point) A quadratic function has its vertex at the...

7. (1 point) A quadratic function has its vertex at the point (-8,1). The function passes through the point (-10,-9). When written in vertex form, the function is f(x) = a(x-h)^2 + k, where: a = h = k = 8. (1 point) Complete the square to find the vertex of the parabola y = x^2 - 8x + 7. Enter your answer as a point (h,k) including parentheses. The vertex is at the point ____ help (points) 9. (1 point) Complete the square to find the vertex of the parabola y = 3x^2 + 30x. Enter your answer as a point (h,k) including parentheses. The vertex is at the point ____ help (points)

Transcript

00:01 So in number seven, you say you have a quadratic function.

00:02 We know the vertex is at the ordered pair negative 8, 1, and we know that the ordered pair negative 10, negative 9 is another point on the graph.

00:09 So in vertex form, which is what they give us, we want to find a, h, and k.

00:14 Well, remember, in vertex form, the ordered pair for the vertex is the ordered pair hk.

00:19 So in this particular case, that would mean that h is negative 8 and k is equal to 1.

00:24 So now we have those two values, so i'll mark them off to the side.

00:27 So h will be negative 8, and k will equal to positive 1.

00:32 All right.

00:33 Well, now we have to find our a value.

00:35 Well, because we know the vertex, we know h and k, and x and f of x represent another or an order to pair on the graph, which we have.

00:42 So to solve for a, we're going to plug in negative 9 for f of x and negative 10 for x.

00:46 So we're going to have negative 9 equal to a times x, which is negative 10, minus h, which is negative 8 quantity squared, plus our k value, which is equal to 1.

00:57 Now we'll simplify.

00:59 Well, these two negatives become a positive.

01:01 So we really have negative 10 plus 8, which is equal to negative 2, squared is positive 4.

01:06 So negative 9 will equal to 4a plus 1.

01:09 So the solve for a will subtract 1 from both sides.

01:12 So negative 10 will equal to 4a.

01:14 So then we'll divide both sides of our equation by 4 and negative 10 divided by 4 is negative 2 .5.

01:20 So perfect.

01:21 Now we have our h, k and a values.

01:25 So this would be the answer to number seven.

01:28 Now i'm going to scroll down here.

01:30 Let's take a look at number eight.

01:31 So it says to complete the square to find the vertex for the given problem.

01:35 So we have y equals x squared minus eight x plus seven.

01:39 So we're trying to rewrite this in our vertex form, which means we need to use completing the square.

01:44 So what i'm going to do is i'm going to block off the first two terms because we have to find what we can add to x squared minus eight x that will make it a perfect square.

01:52 Well, to complete the square, what we do is b divided by 2 square, where b is the coefficient of x, so that would be negative 8...

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