Given

f(x)=ax^2+b (the equation in the picture)

and f(2)=5, f(3)=20,

find a and b.

a = 3, b = - 7

Step-by-step explanation:

Substitute x = 2 into the equation and equate to 5, that is

a(2)² + b = 5

4a + b = 5 → (1)

Substitute x = 3 into the equation and equate to 20

a(3)² + b = 20

9a + b = 20 → (2)

Subtract (1) from (2) term by term to eliminate b

(9a - 4a) + (b - b) = (20 - 5), that is

5a = 15 ( divide both sides by 5 )

a = 3

Substitute a = 3 into either of the 2 equations and solve for b

Substituting in (1)

4(3) + b = 5

12 + b = 5 ( subtract 12 from both sides )

b = - 7

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