Question

Solve this:

Question NO.6 ) If {( – 1, 16), (0, 1), (1, 4) , (2, 25)} $\subset$f, where f : R $\to$R, is a quadratic function, then the function f(x) is

(A) 9x² + 6x +1

(B) 9x² – 6x + 1

(C) 3x² + 2x + 1

(D) 3x² – 2x + 1

Answer 1

$$\begin{gathered} \left\{\left(-1,16\right),\left(0,1\right),\left(1,4\right),\left(2,25\right)\right\}\subset f \\ f:\mathrm{ℝ}\to \mathrm{ℝ} \\ fcontainselements\left(-1,16\right),\left(0,1\right),\left(1,4\right)and\left(2,25\right) \\ f\left(-1\right)=16 \\ f\left(0\right)=1 \\ f\left(1\right)=4andsoon... \\ Sincef\left(x\right)isquadratic \\ Letf\left(x\right)=a{x}^2+bx+c \\ f\left(0\right)=1 \\ 0+0+c=1 \\ c=1 \\ f\left(x\right)=a{x}^2+bx+1 \\ f\left(1\right)=4 \\ a+b+1=4 \\ a+b=3\_\_\_\_\_\_\_\_\left(1\right) \\ f\left(-1\right)=16 \\ a-b+1=16 \\ a-b=15\_\_\_\_\_\_\_\_\_\_\_\left(2\right) \\ Addingequation1and2 \\ 2a=18 \\ a=9 \\ a-b=15 \\ 9-b=15 \\ b=-6 \\ f\left(x\right)=9x^2-6x+1 \end{gathered}$$