It is easier to solve a quadratic equation when it is in standard form because you compute the solution with a, b, and c. However, if you need to graph a quadratic function, or parabola, the process is streamlined when the equation is in vertex form.

Features of quadratic functions Video transcript I have an equation right here. It's a second degree equation. And I know its graph is going to be a parabola. Just as a review, that means it looks something like this or it looks something like that.

Because the coefficient on the x squared term here is positive, I know it's going to be an upward opening parabola. And I am curious about the vertex of this parabola.

And if I have an upward opening parabola, the vertex is going to be the minimum point. If I had a downward opening parabola, then the vertex would be the maximum point.

So I'm really trying to find the x value. I don't know actually where this does intersect the x-axis or if it does it all. But I want to find the x value where this function takes on a minimum value.

Now, there's many ways to find a vertex. Probably the easiest, there's a formula for it. And we talk about where that comes from in multiple videos, where the vertex of a parabola or the x-coordinate of the vertex of the parabola.

So the x-coordinate of the vertex is just equal to negative b over 2a. And the negative b, you're just talking about the coefficient, or b is the coefficient on the first degree term, is on the coefficient on the x term. And a is the coefficient on the x squared term.

So this is going to be equal to b is negative So it's negative 20 over 2 times 5. Well, this is going to be equal to positive 20 over 10, which is equal to 2. And so to find the y value of the vertex, we just substitute back into the equation.

The y value is going to be 5 times 2 squared minus 20 times 2 plus 15, which is equal to let's see. This is 5 times 4, which is 20, minus 40, which is negative 20, plus 15 is negative 5. So just like that, we're able to figure out the coordinate. This coordinate right over here is the point 2, negative 5.

Now it's not so satisfying just to plug and chug a formula like this. And we'll see where this comes from when you look at the quadratic formula.

This is the first term. It's the x value that's halfway in between the roots. So that's one way to think about it. But another way to do it, and this probably will be of more lasting help for you in your life, because you might forget this formula.

It's really just try to re-manipulate this equation so you can spot its minimum point. And we're going to do that by completing the square. So let me rewrite that. And what I'll do is out of these first two terms, I'll factor out a 5, because I want to complete a square here and I'm going to leave this 15 out to the right, because I'm going to have to manipulate that as well.

So it is 5 times x squared minus 4x. And then I have this 15 out here. And I want to write this as a perfect square.

And we just have to remind ourselves that if I have x plus a squared, that's going to be x squared plus 2ax plus a squared. So if I want to turn something that looks like this, 2ax, into a perfect square, I just have to take half of this coefficient and square it and add it right over here in order to make it look like that.

So I'm going to do that right over here.Factor ed Form S o far you have worked with quadratic equations in vertex form and general The answer depends on what you want to know. The vertex form tells you the maximum height and when it occursâ€”in this case, meters Graph each equation and then rewrite it in factored form.

a. y x2 4x 3 b. y x2 5x The standard form of quadratic function is: f(x) = a(x - h)^2 + k, a is different than 0 The graph of f is a parabola whose vertex it is the point (h, k).

Quadratic equation standard form is y = ax^2 + bx + c, with a, b, and c as coefficiencts and y and x as variables. Solving a quadratic equation is easier in standard form because you compute the solution with a, b, and c. Graphing a quadratic function is streamlined in vertex form.

Free functions vertex calculator - find function's vertex step-by-step. Objectives Rewrite a quadratic function in vertex form using completing the square.

Find the vertex of a quadratic function.

Find x-intercepts and y-intercepts of a quadratic function. Write a quadratic function given two points. Slide 3 ; Objectives Solve a word problem involving a quadratic function. Determine how a function has been. The vertex form of a parabola's equation is generally expressed as: $$ y= a(x-h)^ 2 + k $$ (h,k) is the vertex If a is positive then the parabola opens upwards like a regular "U".

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Quadratic standard form |
The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape. |

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Find the vertex of a quadratic function. |

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Lesson 2: Transformations of Quadratics in Vertex Form | That's Parabolic