📈 Quadratic Curves Graph Explorer - Parabola Visualizer
AlgebraWhat's happening? Change a to flip the parabola. Change b to shift the vertex. Change c to move it up/down. Watch how the discriminant determines real vs imaginary roots.
Quadratics: 5-6 questions every year.
JEE tests roots, range, common roots, graph. D = b^2-4ac is key.
Key formulas
Quadratic Curves Formulas
Quadratic formula
x = (-b +/- sqrt(D)) / 2a
D = b^2-4ac
Discriminant
D = b^2 - 4ac
D>0: 2 real, D=0: equal, D<0: complex
Vertex
f(x) = a(x-h)^2 + k
h = -b/2a, k = f(h)
Sum/product
alpha+beta = -b/a, alpha*beta = c/a
Vieta's formulas
Step-by-step problem solving
How to solve maths problems in JEE
- Identify a, b, c
- Calculate D = b^2-4ac
- If D>=0: x = (-b +/- sqrt(D))/2a
- For range: vertex form
Common JEE mistakes
What students get wrong
Sign error -b
Subtracting negative b gives +b
Graph direction
a>0: up, a<0: down
D<0 no real roots
Graph doesn't cross x-axis
Range wrong way
a>0: [k,inf), a<0: (-inf,k]
FAQs
Quadratic Curves Questions
Imaginary roots?
D < 0. No x-axis intersection.
Find range?
Vertex form. a>0: [k,inf), a<0: (-inf,k]
Common roots?
Resultant = 0
More than 2 roots?
No. Degree 2 = exactly 2 roots.