VG1
funksjoner
Quiz
What is a quadratic function?
A quadratic function produces a parabola — the characteristic U-shape seen everywhere from bridges to projectile calculations.
🎮 Try it yourself — interactive!
Drag the sliders and see the parabola change. The quadratic formula solved step by step.
→ Open interactive parabola
Drag the sliders and see the parabola change. The quadratic formula solved step by step.
→ Open interactive parabola
The formula
f(x) = ax² + bx + c
- a determines opening direction (a ≠ 0)
- b affects the position
- c is the y-intercept
a > 0 → parabola opens upward ☺
a < 0 → parabola opens downward ☹
a < 0 → parabola opens downward ☹
Vertex
x = -b / (2a)
Example: f(x) = x² - 4x + 3
Vertex: x = 4/2 = 2, f(2) = -1 → vertex at (2, -1)
Finding zeros — the quadratic formula
x = (-b ± √(b²-4ac)) / (2a)
Discriminant D = b² - 4ac:
D > 0 → two zeros · D = 0 → one zero · D < 0 → no zeros
D > 0 → two zeros · D = 0 → one zero · D < 0 → no zeros
I think, therefore I am — and in mathematics I found the clearest form of true knowledge.
— René Descartes (1596–1650)
🧠 Test yourself
Question 1 of 3
Which direction does f(x) = -2x² + 3 open?