Math kitchen- Quadratic formula project

Added: 2026-05-06

[00:00:00]You're hungry, man? Yeah, I'm a little hungry.

[00:00:03]Some takeout would be great. Yeah, yeah.

[00:00:05]I'm broke. What are we going to do now?

[00:00:08]Do you remember that secret recipe that grandma shared with me? The recipe for root cake?

[00:00:12]>> Yeah, I think I know. Yeah. Let's go make it.

[00:00:16]We're going to keep that recipe.

[00:00:18]Oh.

[00:00:21]So nice of my grandma to share me this recipe to her favorite boy.

[00:00:31]Okay, root cake recipe.

[00:00:33]What in the world is this?

[00:00:36]Oh, right.

[00:00:38]Grandma was a mathematician. Um and it is a quadratic. Oh, good thing I'm exploring quadratics in my math class.

[00:00:46]Y = x² - 5x + 6 and x is equal to the sugar.

[00:00:53]Nice.

[00:00:56]But how much sugar?

[00:00:58]What is this other part of the recipe?

[00:01:00]Secret tip.

[00:01:02]The recipe only works when y = 0. Hmm, let me use my brain real quick.

[00:01:08]All right, so we got the flour and the butter and the eggs. But I can't cook this up without knowing exactly how much sugar I need to add.

[00:01:16]Hmm.

[00:01:17]So, it's called root cake. Meaning I could probably find the roots. Maybe that'll tell me how much sugar I need to put. Y = x² - 5x + 6 and uh it only works when y is equal to zero.

[00:01:30]So, we can set this up like this. Zero is equal to x² - 5x + 6.

[00:01:35]And the only way we can find x is factoring it. So, um you use this quadratic formula, which is x is equal to -b plus or minus root uh b² - 4ac the whole over 2a to uh find the roots of this.

[00:01:48]So, uh our equation is written in a standard form for a quadratics, uh which is ax² + bx + c. And it's shown that uh we need one stick of butter - 5x + 6 cups to get zero.

[00:02:03]So, we can do some plugging in and we see that this is -5 and this is -b. So, to write that, you're going to have to write it like minus of minus five.

[00:02:12]Um so for the first one, we can do the plus cuz it's plus or minus the square root of -5 squared minus four times uh one times six all over two times one.

[00:02:29]So, let's see. So, this this becomes five plus 25 minus So, we're going to do some order of operations here. We have multiplication uh minus 24 divided by two.

[00:02:48]So, we get five plus root of one over two, which is equal to six over two, which is three.

[00:02:56]So, this shows that one value of sugar that can be used is three.

[00:03:03]Since we already used the plus from this equation, we can now use the minus to find the second amount of sugar we can add. Um so negative negative five we can simply just minus here then So, it's 5 minus 1 over 2, which gives you two.

[00:03:33]So, we got x is equal to three from the plus and x is equal to two from the minus. This means if we add 3 g of sugar and or 2 g of sugar, the cake will turn out just fine. To construct a parabola with this equation, I need these points.

[00:03:46]So, um we can see in standard form the y-intercept, which is 0,6.

[00:03:51]And then we already found the two roots, which is also the x-intercepts, uh which is two and three. In the middle of two and three is 2.5, which if we can use to find the vertex, uh which is -0.25. We found that by plugging 2.5 into the x value of the equation and then solving there from that on. So, this is the parabola of the equation.

[00:04:16]Oh, and I forgot to add that um to find the other point of the parabola parabola to make it symmetric to this y-intercept, you need to use the same y-coordinate but the difference of these is what you need to figure out for the x. So, for this, this would be five cuz the difference in x-axis with the y-intercept in this point right here is two and this the difference should be two here with and 3 + 2 gives you five.

[00:04:37]So, this is 5,6.

[00:04:43]Ah, grandma sure did challenge me with this recipe. But now we know the perfect amount of sugar, let's get baking.

[00:04:49]I don't even like cake.

[00:04:51]We don't even have any cake.

[00:04:53]We don't have any cake.

[00:04:55]>> [music] >> I don't even have any cake. I don't have I don't even have any cake. I don't have any cake. I don't have I don't have