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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.

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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 calculator will find either the equation of the parabola from the given parameters or the axis of symmetry, focus, vertex, directrix, Operations over Complex Numbers in Trigonometric Form.

De Moivre's Formula; If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. write sin x (or even better sin(x.

Learn about the four conic sections and their equations: Circle, Ellipse, Parabola, and Hyperbola. Since the equation is in vertex form, the vertex will be at the point (h, k).

Step 2: You can solve for x by using the square root principle or the quadratic formula (if you simplify the problem into the correct form). Step 4: Graph the parabola using the points found in steps 1 – 3.

Example 1 – Graph. After watching this video lesson, you will be able to write the equation of a parabola in standard form when given just two important points from the parabola.

Ask Math Questions you want answered Share your favorite Solution to a math problem Share a Story about your experiences with Math which could inspire or help others. Write the equation with y 0 on one side: y 0 = x 0 2 4 − x 0 + 5 This equation in (x 0, y 0) is true for all other values on the parabola and hence we can rewrite with (x, y).

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Equations of a Parabola: Standard to Vertex Form and Back Again | Montessori Muddle