Question

f(x) = ax²+bx
f(-2) = 20 and f(4) = 32
find the values of a and b

Answer 1

Answer:

The answer is $a=3,b=-4$

Step-by-step explanation:

Given function is $f(x)=ax^2+bx$

First condition is $f(-2)=20$

$\Rightarrow a(-2)^2+b(-2)=20\\\Rightarrow 4a-2b=20\\\Rightarrow 2a-b=10 ....(1)$

Second condition is $f(4)=32$

$\Rightarrow a(4)^2+b(4)=32\\\Rightarrow 16a+4b=32\\\Rightarrow 4a+b=8...(2)$

Now add (1) and (2)

$\Rightarrow 2a-b+4a+b=10+8\\\Rightarrow 6a=18\Rightarrow a=3$

Using (2)

$\Rightarrow 4(3)+b=8\Rightarrow b=8-12=-4$

Hence $a=3,b=-4$