Get the solution to "Find the equation of the quadratic function f..."

Marvin Mccormick

Answered question

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 (x) = a x^{2} + b x + c

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

∴ 4 = a x {(- 1)}^{2} + b x (- 1) + c

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

8 = a x {(- 3)}^{2} + b x (- 3) + c

\Rightarrow 9 a - 3 b + c = 8 (I I)

5 = a \cdot x^{2} + b x 0 + c

\Rightarrow c = 5 (I I I)

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

a - b + 5 = 4 \Rightarrow a - b = - 1 - (I V)

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

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

\Rightarrow 3 a - b = 1 - (V)

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

- 2 a = - 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 (x) = a x^{2} + b x + c,

we get

f (x) = x^{2} + 2 x + 5

Jeffrey Jordon

Expert2022-01-14Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?