Quadratics

Question 1

Quadratic Formula

Answer 1

-b±√b²-4ac / 2a

Question 2

Standard and Completed square form of Quadratic equation

Answer 2

y= ax² + bx + c
y= a(x+h)² + k

Question 3

Formula to find quadratic equation if roots (values of x) are given

What if curve is maximum?

Answer 3

Go reverse factorisation or…

Formula: x² - x(Sum of roots) + (Product of roots)

If maximum, formula: -[x² - x(sum of roots) + (product of roots)]
Try x = 4 & x = 5 if curve is minimum
Try x = 2 & x = 1 if curve is maximum
Check ans using calc.

Question 4

Expansion of a(x+h)² + k
Turning point
Line of symmetry

Answer 4

ax² + 2ahx + ah² + k
(-h,k)
x = x coordinate of T.P , i.e -h
It’s x cuz it’s a vertical line (quite obviously)

Question 5

4 methods of calculating turning point + تفاصيلها

Answer 5

1. Calculator midpoint of roots [(x1+x2) ÷ 2] & put the answer in the quadratic eq for y coordinate
2. (-h,k) If a(x+h)² + k
3. Formula: [-b/2a , (4ac -b²) / 4a] if y = ax² + bx + c
4. Differentiation, by putting dy/dx = 0

Question 6

Discriminant is…

Answer 6

b² - 4ac

Question 7

Real & Distinct roots

Answer 7

b² - 4ac > 0
Two solutions

Question 8

Real and equal roots

Answer 8

b² - 4ac = 0
One solution
Condition of tangency

Question 9

Imaginery roots
Complex roots
No real roots

Answer 9

b² - 4ac < 0
No solution
Minimum curve entirely above x axis
Maximum curve entirely below x axis

Question 10

Real roots

Answer 10

b² - 4ac ≥ 0
Question may say: y = … “meets” this and that…
1 or 2 solution

Question 11

Steps To Solve Discriminants ke questions (ratta)

Answer 11

1. Start solving 2 equation simultaneously (Sometimes not needed)
2. You will get stuck so use discriminant accordingly
3. If b² - 4ac = 0, solve & find answers
4. If no equal to solve the inequality (could be linear in quadratic)