Rewrite each equation in vertex form. Then find the vertex of the graph. y=(1)/(2) x^2-5 x+12

Name: Problem 35, Chapter 5: Algebra 2
Uploaded: 2019-11-26T02:48:09-08:00
Duration: 3 min 43 s
Channel: Martha Richards
Description: Rewrite each equation in vertex form. Then find the vertex of the graph. y=(1)/(2) x^2-5 x+12

Rewrite each equation in vertex form. Then find the vertex...

Key Concepts

Quadratic Function

A quadratic function is a second-degree polynomial usually expressed in the form ax^2 + bx + c, where a, b, and c are constants and a ? 0. This type of function exhibits a parabolic graph that opens upward when a is positive and downward when a is negative, representing important concepts in algebra and the study of functions.

Vertex Form

The vertex form of a quadratic function is expressed as y = a(x - h)^2 + k. This form directly reveals the vertex (h, k) of the parabola, making it easier to determine the maximum or minimum point and understand transformations such as translations and reflections from the graph’s standard position.

Completing the Square

Completing the square is a method used to rewrite a quadratic expression into a perfect square plus a constant. This technique is essential for converting a quadratic in standard form to vertex form, as it systematically adjusts the quadratic by adding and subtracting appropriate terms to create a perfect square trinomial.

Vertex of a Parabola

The vertex of a parabola is the point where the curve reaches its maximum or minimum value, directly corresponding to the coordinates (h, k) in the vertex form equation. Identifying the vertex is crucial in graphing quadratic functions, as it helps in understanding the function’s symmetry, direction, and optimal value.

Transcript

00:01 Provided with this equation here and we're asked to put this into vertex form and find the vertex.

00:07 So what we do is we're going to take this portion here and do a complete square and also we have to get a one in front of this x.

00:17 So because what we're trying to make this equation look like is a x minus h squared plus k.

00:29 So this is vertex.

00:30 So this is vertex.

00:30 Form.

00:31 So the first thing we're going to do is we're going to take this one -half x squared minus 5x plus 12.

00:43 And what we're going to do is we're going to just take this portion here and we're going to pull out a one -half.

00:51 When i factor out this one -half, i get an x squared first.

00:56 And then i need a minus 10x because in order to, if i multiply this back out, if i multiply a minus 10x by one -half, i get back to that negative 5.

01:08 So now i'm going to use this value here to figure out how to complete the square.

01:15 So i do that by taking the negative 10, dividing by 2, and squaring that.

01:27 So i get a negative 5 squared, which is 25.

01:37 So here i'm going to add 25.

01:39 But remember i multiplied this by a one -half.

01:46 So i'm adding 25 over two really to this.

01:52 So i'm going to out here subtract 25 over 2...

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