Graphing Parabolas
Parabolas of the form y = a(x-h)² + k have vertex (h, k), axis of symmetry x = h, and open upward when a > 0 or downward when a < 0.
What You Need to Know
Parabolas of the form y = a(x-h)² + k have vertex (h, k), axis of symmetry x = h, and open upward when a > 0 or downward when a < 0.
Key Concept Diagram
Vertex form y = a(x-h)² + k gives vertex (h, k) directly
Axis of symmetry is the vertical line x = h through the vertex
If a > 0 the parabola opens upward (minimum at vertex); if a < 0 it opens downward (maximum)
x-intercepts are found by setting y = 0; y-intercept by setting x = 0
Key Vocabulary
Vertex
The turning point (maximum or minimum) of a parabola
Axis of symmetry
The vertical line x = h that divides the parabola into two mirror-image halves
x-intercept
A point where the parabola crosses the x-axis (y = 0)
Turning point form
y = a(x-h)² + k; another name for vertex form
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the vertex of y = 2(x - 3)² + 1?
Question 2
The parabola y = -(x+2)² - 5 opens:
Question 3
What is the axis of symmetry of y = 3(x + 4)² - 7?
Key Concepts Summary
- ●Vertex form y = a(x-h)² + k gives vertex (h, k) directly
- ●Axis of symmetry is the vertical line x = h through the vertex
- ●If a > 0 the parabola opens upward (minimum at vertex); if a < 0 it opens downward (maximum)
- ●x-intercepts are found by setting y = 0; y-intercept by setting x = 0