Question

which function is best represented by this graph?A) f(x) = -3x² + 2x + 1 B) f(x) = 3x² + 2x - 4C) f(x) = x² + x - 4D) f(x) = x² + 2x - 3

Answer 1

Answer:

From the graph, the roots of the equation are given below as

$\begin{gathered} x=-3 \\ x=1 \end{gathered}$

These are the points where the curve cuts the x-axis

The y-intercepts of the graph is given below as

$(0,-3)$

Concept:

To find the equation of the graph, we will use the formula below

$\begin{gathered} f(x)=a(x+3)(x-1) \\ x=0,y=-3 \\ -3=a(0+3)(0-1) \\ \frac{-3}{-3}=\frac{-3a}{-3} \\ a=1 \end{gathered}$

Hence,

By substituting the values, we will have

$\begin{gathered} f(x)=a(x+3)(x-1) \\ f(x)=1(x+3)(x-1) \\ f(x)=x^2-x+3x-3 \\ f(x)=x^2+2x-3 \end{gathered}$

Hence,

The function of the graph is

$f(x)=x^2+2x-3$

OPTION D is the right answer