Question

What is the equation, In factored form, of the quadratic function shown in the graph?

Answer 1

Given:

The graph of a quadratic function.

To find:

The equation of the quadratic function in factored form.

Solution:

From the given graph it is clear that the graph of the function intersect the x-axis at point (-3,0) and (2,0).

Since -3 and 2 are the zeros of the function, therefore (x+3) and (x-2) are the factors of the required quadratic function.

Now, the function can be written as:

$f(x)=a(x+3)(x-2)$             ...(i)

The graph of the function intersect the y-axis at (0,-6). Substituting $x=0,f(x)=-6$ in (i), we get

$-6=a(0+3)(0-2)$

$-6=a(3)(-2)$

$-6=-6a$

$\dfrac{-6}{-6}=a$

$1=a$

Substituting $a=1$ in (i), we get

$f(x)=1(x+3)(x-2)$

Therefore, the required function is $f(x)=1(x+3)(x-2)$.