what can i do if a quadratic function is in the form 2x^2 + y = 3

[abel muroi]

i was given the problem 2x² + y = 3 and was told to put the equation in standard form so i can find the vertex

so first i decided to put y by itself on one side

y = -2x² + 3

but since i cant really factor this, im not sure what to do next.

 

[HallsofIvy]

i was given the problem 2x² + y = 3 and was told to put the equation in standard form so i can find the vertex

so first i decided to put y by itself on one side

y = -2x² + 3

but since i cant really factor this, im not sure what to do next.

I presume that, since you are asked to put it in "standard form", you know what that means:y= a(x- b)^2+ c. You should also know that \(\displaystyle x^2= (x- 0)^2\).

 

[abel muroi]

I presume that, since you are asked to put it in "standard form", you know what that means:y= a(x- b)^2+ c. You should also know that \(\displaystyle x^2= (x- 0)^2\).

so that mean that the standard form of the equation i gave you is -2(x - 0)² + 3

so does that also mean that the vertex is (0, 3) ?

 

[HallsofIvy]

so that mean that the standard form of the equation i gave you is -2(x - 0)² + 3

so does that also mean that the vertex is (0, 3) ?

What is the definition of "vertex" of a parabola?

 

[abel muroi]

What is the definition of "vertex" of a parabola?

a vertex is where two or more lines meet right?

that is the definition i think, but the vertex of a parabola is the point that divides the parabola evenly.

 

[Steven G]

so that mean that the standard form of the equation i gave you is -2(x - 0)² + 3

so does that also mean that the vertex is (0, 3) ?

Yes, you have the correct vertex. You really should write y=-2(x - 0)² + 3 or simply y= -2x² + 3

 

[stapel]

a vertex is where two or more lines meet right?

No; this is an "intersection". What source told you that the vertex was where two lines met? :shock:

the vertex of a parabola is the point that divides the parabola evenly.

How have you defined "dividing" a parabola? How have you defined "evenly"?

To learn the usual process for finding the vertex, try here. To learn the names of the parts of a parabola, and how they are defined, try here.

 

[Ishuda]

I had always (well at least for a long time) understood a vertex (of an angle for example) was the the place where two lines met and, as a different meaning, that a (normal, i.e. un-tilted) parabola had a line of symmetry that passed through the vertex and divided the parabola evenly.

 

[HallsofIvy]

In general, a "vertex" for a curved line is a point where the curvature is a local extremum, either a maximum of a minimum. For example, an ellipse has four vertices, at the ends of the major and minor axes. At the ends of the major axis, the curvature is a local maximum. At the ends of the minor axis, the curvature is a local minimum.

 

[Ishuda]

In general, a "vertex" for a curved line is a point where the curvature is a local extremum, either a maximum of a minimum. For example, an ellipse has four vertices, at the ends of the major and minor axes. At the ends of the major axis, the curvature is a local maximum. At the ends of the minor axis, the curvature is a local minimum.

For a curved surface, yes. But, in general, it depends on the field you are talking about and who you ask. For example, looking at
http://www.mathopenref.com/vertex.html
we have

Definition: The common endpoint of two or more rays or line segments

Vertex typically means a corner or a point where lines meet. For example a square has four corners, each is called a vertex. The plural form of vertex is vertices. (Pronounced: "ver - tiss- ease"). A square for example has four vertices.
...
In solid geometry, a vertex is the point where three or more edges meet.
...
A parabola is the shape defined by a quadratic equation. The vertex is the peak in the curve as shown on the right ...

EDIT: And, in a broad sense, you could define the x co-ordinate of the vertex of a parabole as the line defined by the meeting of the two lines which are tangent to the parabola at equal distances from the line of symmetry.