### Concept (1)

When graphing a quadratic equation, the resulting shape is not a straight line, but instead a shape called a parabola. Parabolas vary in direction and shape. The lowest or highest point in a parabola is called a vertex, which lies on the axis of symmetry. If the leading coefficient of the term to the second degree is positive, the parabola faces up. If it is negative, the parabola faces down.

### Sample Problems (8)

Need help with "Introduction to Parabolas" problems? Watch expert teachers solve similar problems to develop your skills.

Graph the parabolas:

f(x) = (x − 1)²
f(x) = 2x²
f(x) = -x²
f(x) = (x + 3)²
f(x) = ½x²
###### Problem 1
How to transform the graph of a parabola.

Graph:

f(x) = -3(x + 2)² + 4
###### Problem 2
How to use vertex form to graph a parabola.
a) Give any equation for a parabola with vertex (-3,-2)
b) That also passes through (-2,4)
###### Problem 3
How to write the equation of a parabola given the vertex.

Determine 'a' and 'k' so that (-3,2) and (0,11) lie on y = a(x + 2)² + k

###### Problem 4
How to write the equation for a parabola given specific points.
###### Problem 5
How to write the equation for a parabola from a graph or from the vertex and one other point
###### Problem 6
Using transformations to sketch parabolas in vertex form, including those with "a" value not one
###### Problem 7
Using transformations to sketch parabolas in vertex form
###### Problem 8
Writing equations for equations back and forth between standard and vertex form