Graphing Parabolas
A parabola is the U-shaped graph of a quadratic function y = ax^2 + bx + c. The shape, direction, and position depend on the values of a, b, and c.
What You Need to Know
Key Concept Diagram
The graph of y = ax^2 is a parabola; if a > 0 it opens upward, if a < 0 it opens downward
The vertex is the turning point of the parabola (minimum or maximum)
The axis of symmetry is a vertical line through the vertex
The y-intercept is found by substituting x = 0
Key Vocabulary
Parabola
The curved graph of a quadratic function; U-shaped or inverted-U
Vertex
The turning point of a parabola; the minimum or maximum point
Axis of symmetry
The vertical line that divides the parabola into two mirror halves
y-intercept
The point where the parabola crosses the y-axis
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
For y = -3x^2, which way does the parabola open?
Question 2
What is the vertex of y = x^2 - 4?
Question 3
What is the y-intercept of y = 2x^2 + 3x - 5?
Key Concepts Summary
- ●The graph of y = ax^2 is a parabola; if a > 0 it opens upward, if a < 0 it opens downward
- ●The vertex is the turning point of the parabola (minimum or maximum)
- ●The axis of symmetry is a vertical line through the vertex
- ●The y-intercept is found by substituting x = 0