When the vertex is the highest point it is called a?

That Highest Point? It’s Called a Maximum.

Okay, so you’re looking at a parabola – that U-shaped curve you probably remember from math class. The vertex? That’s the super important point where the curve changes direction. Think of it like a rollercoaster reaching the top of a hill before plunging down. Now, sometimes that vertex is the lowest point, like a valley. But what if it’s the highest point? Well, that’s when we call it a maximum. Simple as that!

Let’s break it down a little further. Parabolas are basically the visual representation of quadratic functions. Remember those? They can look a little intimidating, but don’t worry, we’ll keep it simple. You might see them written in a couple of different ways:

• Like this: y = ax2 + bx + c – that’s the standard form.
• Or like this: y = a(x – h)2 + k – this one’s called vertex form because it tells you the vertex is at the point (h, k). Pretty neat, huh?

That little “a” in front is super important. It’s like the steering wheel for the parabola. If “a” is positive, the parabola opens upwards, like a smile. That means you’ve got a minimum point at the bottom. But if “a” is negative? Frown time! The parabola opens downwards, and you’ve got a maximum at the top.

So, how do you actually find that maximum point? Good question! If you’re lucky enough to have the equation in vertex form, you’re golden! It’s right there in the equation: (h, k). But what if you’ve got that standard form equation? No sweat! Here’s the trick:

There’s even a way to do it using calculus, if you’re feeling fancy. You take the derivative, set it equal to zero, and solve for x. But let’s not get bogged down in calculus right now.

Okay, so why should you even care about all this? Well, it turns out parabolas and maximums pop up all over the place in the real world. Think about it:

• Ever thrown a ball? The path it takes through the air is a parabola! The maximum point? That’s how high the ball goes.
• Engineers use parabolas to design all sorts of things, like bridges and arches. They need to know where the maximum stress will be so they can make sure the structure is strong enough.
• Satellite dishes and telescopes? Yep, they use parabolic shapes to focus signals. The maximum point helps them get the clearest picture possible.

I remember back in college, I was working on a project involving solar energy. We were using parabolic troughs to focus sunlight onto a pipe filled with water, which would then heat up and generate electricity. It was amazing to see how a simple mathematical concept like a parabola could be used to create clean energy!

So, to recap: the vertex is the turning point of a parabola. If the parabola opens downwards, that vertex is the highest point, and we call it a maximum. It’s a simple concept, but it has powerful applications in all sorts of fields. And who knows? Maybe understanding parabolas will even help you throw a football a little further!