Marvin Mccormick

2021-08-20

Find the equation of the quadratic function f whose graph is shown below

Caren

Skilled2021-08-21Added 96 answers

The graph of function f(x) is shown

$f\left(x\right)=a{x}^{2}+bx+c$

Since the graph pases from point (-1,4), (-3,8) and (0,5)

$\therefore 4=ax{(-1)}^{2}+bx(-1)+c$

$\Rightarrow a-b+c=4-\left(I\right)$

$8=ax{(-3)}^{2}+bx(-3)+c$

$\Rightarrow 9a-3b+c=8\left(II\right)$

$5=a\cdot {x}^{2}+bx0+c$

$\Rightarrow c=5\left(III\right)$

from equation (I) and(III), we get

$a-b+5=4\Rightarrow a-b=-1-\left(IV\right)$

and from equation (II) and (III), we get

$9a-3b+5=8\Rightarrow 9a-3b=3$

$\Rightarrow 3a-b=1-\left(V\right)$

from equation (IV)-equation(V) we get,

$-2a=-2\Rightarrow a=1$

put a=1 in equation(IV), we get

$1-b=-1\Rightarrow b=2$

Now substitute a=1, b=2 and c=5 in the function$f\left(x\right)=a{x}^{2}+bx+c,$ we get

$f\left(x\right)={x}^{2}+2x+5$

Since the graph pases from point (-1,4), (-3,8) and (0,5)

from equation (I) and(III), we get

and from equation (II) and (III), we get

from equation (IV)-equation(V) we get,

put a=1 in equation(IV), we get

Now substitute a=1, b=2 and c=5 in the function

Jeffrey Jordon

Expert2022-01-14Added 2605 answers

Answer is given below (on video)

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