Things i forgot how to do/unsure about. Porabola stuff

  • Thread starter MrNonexistent
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In summary, the conversation discusses finding the vertex and x-intercepts in terms of variables a, h, and k, and how these values affect the graph of a quadratic equation. The formula y = A(x - h)^2 + k is used to determine the vertex and the x-intercepts can be found by setting y = 0 and solving for x. The values of a, h, and k determine the shape and position of the parabola, with a larger a resulting in a narrower parabola and a negative a causing the parabola to be inverted.
  • #1
MrNonexistent
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Homework Statement


1) find the vertex, 2) find the x intercepts in terms of a, h, and k, 3) explain how values of a, h, and k affect the graph


Homework Equations


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


The Attempt at a Solution


1) (H,K)
2) aaaahhh i don't know... i just forgot.
3) A determines how wide it is, with a bigger a making a skinnier parabola, a smaller A making a wider parabola, and a negative a making it go upside down. H moves the vertex along the x axis, and K moves it along the Y axis.


is the ones i answered right? also. i would really appreciate a hint as to how to find out 2.

thanks guys
 
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  • #2
2. In order for you to be on the x-axis, set y=0. So from there, just solve for x. Whenever a problem says solve "x" in terms of a, b, c ... etc., they just want you to have it look like x = a, b, c.

1 & 3 are good.
 
  • #3
ooo... hm let's check it out.
 
  • #4
im getting that

A(x-h)^2 = [tex]\sqrt{-k}[/tex]

gives you one and if you subtract -K from this answer, you get the other x axis.
 
  • #5
x = [tex]\frac{\sqrt{-k}}{A} \pm AH[/tex]


is that right? i am so braindead.
 

FAQ: Things i forgot how to do/unsure about. Porabola stuff

How do I graph a parabola?

To graph a parabola, you will need to identify the vertex, focus, and directrix of the parabola. The vertex is the point on the parabola where it changes direction, the focus is a point inside the parabola, and the directrix is a line that is perpendicular to the axis of symmetry of the parabola. Once you have these points, you can plot them on a coordinate plane and then sketch the curve of the parabola connecting them.

What is the equation of a parabola?

The standard form of the equation for 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 b and c affect the position of the parabola on the coordinate plane. There are also other forms of the equation, such as vertex form and intercept form, that can be used depending on the given information about the parabola.

How do I find the axis of symmetry of a parabola?

The axis of symmetry of a parabola is a vertical line that passes through the vertex and divides the parabola into two equal halves. To find the axis of symmetry, you can use the formula x = -b/2a, where a and b are the coefficients in the standard form equation of the parabola. This will give you the x-coordinate of the vertex, which is also the x-coordinate of the axis of symmetry.

What is the significance of the focus and directrix in a parabola?

The focus and directrix are important elements of a parabola because they help define its shape and position on the coordinate plane. The focus is the point that is equidistant from all points on the parabola, and the directrix is the line that is perpendicular to the axis of symmetry and intersects the focus. Together, these points and lines determine the size and location of the parabola.

How do I solve problems involving parabolas?

To solve problems involving parabolas, you will need to use the properties and equations related to parabolas. This may include finding the vertex, focus, and directrix, solving systems of equations involving parabolas, or using the quadratic formula to find the roots of a parabola. It is important to understand the concepts and formulas related to parabolas in order to successfully solve problems involving them.

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