Question

How do you determine the vertex and direction when given a quadratic function?

Answer 1

There are two forms a quadratic function could be written in: standard or vertex form. Here are the following ways you can determine the vertex and direction dependent on the form:

Standard Form (`f(x)=ax^2 + bx + c`)
1. Direction of the parabola can be determined by the value of a. If a is positive, then the parabola faces up (making a u shaped). If a is negative, then the parabola faces down (upside down u).
2. Vertex can be found by `x= -b/(2a)` and then plugging in that value to find y.
Here is an example:
`y = -2x^2 + 4x - 3`, Faces downward since a = -2.
to find the vertex: `x= (-4)/(2(-2))=(-4)/ (-4) = 1`
then plug that value into the equation`y = -2x^2 + 4x - 3`
`y = -2(1)^2 + 4(1) - 3`
`y = -2(1) +4(1) - 3`
`y = -2 + 4 -3`
`y = -1`
Vertex is (1,-1)

Vertex Form (`y=a(x-h)^2 +k`)
1. Direction of the parabola can be determined by the value of a. If a is positive, then the parabola faces up (making a u shaped). If a is negative, then the parabola faces down (upside down u).
2. Vertex is (h,k).
Here is an example:
`y = -3(x-2)+6` Faces down since a = -3 and the vertex is (2, 6).