What is the significance of the equation y=2(x-4)^2-3?

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In summary, the conversation is about a first-year university student seeking help with a math question involving the equation y=2(x-4)^2-3. The student has used the formula b+/- b^2 -4ac to solve the equation, but is unsure if the result (16+/- square root of 24/4) is correct. They also mention converting the equation to ax^2+bx+c=0 form and finding the vertex and direction of the parabola. The expert summarizes that the student can find a lot of information from the given equation, but asks for clarification on what specific information the student needs.
  • #1
DethRose
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Im In a 1st Year University math class and its been a while since i did this stuff and can't remember if I am doing this question right so any help would be much appreciated.

The question is to find all the info from the equation y=2(x-4)^2-3

I used the b+/- b^2 -4ac... equation and ended up getting 16+/- square root of 24/4.

This gives an odd number (5.22474, 2.77525) so i don't think it is right. When i apart the original equation to make into ax^2+bx+c=0 form i did 2(x^2-8x+16)-3=0 and i am not sure if that is correct either or if it should be multiplies without brackets.

Thanks for any help
 
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  • #2
I haven't checked your working out, but I don't see what's wrong with the numbers it gives? You were never given an indication the numbers would be pretty.
 
  • #3
The parabola you have is written in a very nice form...

y = a(x - h)^2 + k

"The question is to find all the info from the equation "... :-/

All the info? Be more specific. From this form it is easy to find the Vertex (h,k). You can also tell whether or not it will be opening up, or down. If a >0 then the parabola will open up. If a<0 then the parabola will be opening down.

Furthermore, a will tell you how thin or fat your parabola will be. If 0<|a|<1 your parabola will be fatter than the parabola y=x^2. If |a|>1 your parabola will be thinner than y = x^2.

As you can see one can tell a lot by the equation given without having to do much work. Is there further information that you need from the equation given? If so, what?
 

1. What is a parabola?

A parabola is a type of curve that is formed by the intersection of a plane and a cone when the plane is parallel to one of the cone's sides. It is a symmetrical curve that resembles a U-shape or a smile.

2. What are the main characteristics of a parabola?

The main characteristics of a parabola are its vertex, focus, and directrix. The vertex is the point where the parabola makes its sharpest turn, and it lies on the axis of symmetry. The focus is a fixed point inside the parabola, and the directrix is a line that is perpendicular to the axis of symmetry and passes through the focus.

3. How do you graph a parabola?

To graph a parabola, you will need to identify its vertex, focus, and directrix. Plot these points on a coordinate plane and then use the shape of the parabola to plot additional points. You can also use a table of values to plot points and create a smooth curve connecting them.

4. What is the equation of a parabola?

The general equation of a parabola is y = ax^2 + bx + c, where a, b, and c are constants. The value of a determines the direction and shape of the parabola, while the values of b and c determine the position of the parabola on the coordinate plane.

5. What are some real-life applications of parabolas?

Parabolas have many real-life applications, such as in architecture, engineering, and physics. They are used to design structures such as arches, bridges, and satellite dishes. They are also used in projectile motion calculations, such as the trajectory of a thrown ball or a launched rocket.

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